Question 1 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationEasy
What is the largest prime factor of 120?
Official Correct Answer: C. Factorize 120 into primes: $120 = 2^3 \times 3 \times 5$. The largest prime factor is 5.
Number Systems • Factors & Factorisation Practice Drills (84 Qs)• Official Answer Keys
CAT Factorisation & Number of Factors Practice Questions (80+ Questions)
Prime Factorisation, Number of Factors, Sum of Factors, Even/Odd Factors, and Co-Prime Pair Counting
84 Total Questions
MCQ: 76 (+3 / -1)
TITA: 8 (0 Negative Penalty)
Core Formulas & Shortcut Matrix: Factors & Factorisation Practice Drills
Sum of FactorsFormula #1
S = \frac{p^{a+1}-1}{p-1} × \frac{q^{b+1}-1}{q-1}
For prime factorisation N = p^a q^b.
Product of FactorsFormula #2
\text{Product} = N^{\text{Total Factors} / 2}
Pairs up divisors from ends.
Exam Hall Traps & Speedbreakers to Avoid
- •Including 2^0 when counting EVEN factors (even factors require power of 2 to be at least 1).
Bite-Sized Practice Sets (9 Modules Available)
Authentic CAT BlueprintSolve in structured 20–25 question practice sets with instant accuracy benchmarking and solution checks. Sets 01 & 02 are completely free.
12 QuestionsFree Pass
Set 01: Factorisation
Difficulty: Easy
12 QuestionsPro Pass
Set 02: Factorisation
Difficulty: Moderate
7 QuestionsPro Pass
Set 03: Factorisation
Difficulty: Hard
12 QuestionsPro Pass
Set 04: Factorisation
Difficulty: Moderate
12 QuestionsPro Pass
Set 05: Factorisation
Difficulty: Easy
8 QuestionsPro Pass
Set 06: Factorisation
Difficulty: Easy
7 QuestionsPro Pass
Set 07: Factorisation
Difficulty: Moderate
8 QuestionsPro Pass
Set 08: Factorisation
Difficulty: Easy
6 QuestionsPro Pass
Set 09: Factorisation
Difficulty: Hard
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Official Exam Questions & Explanations (25 of 84)
Sorted in official convenor sequenceQuestion 2 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
What is the smallest positive integer that has exactly 12 factors?
Official Correct Answer: B. For a number to have 12 factors, its prime factorization must be of the form $p^{11} , p^5q , p^3q^2 , or $pqr$ where $p, q, r$ are distinct primes. The smallest number with the form $p^5q$ is $2^5 \times 3 = 48$. Thus, 48 is the smallest such number.
Question 3 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationHard
What is the number of distinct prime factors of 360?
Official Correct Answer: C. Factorize 360: $360 = 2^3 \times 3^2 \times 5$. The distinct prime factors are 2, 3, and 5. Thus, there are 3 distinct prime factors.
Question 4 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationEasy
What is the smallest integer greater than 1 that has exactly 3 factors?
Official Correct Answer: D. A number has exactly 3 factors if it is the square of a prime number. The smallest such number is $2^2 = 4 , but 4 has 3 factors (1, 2, 4). The next is $3^2 = 9 , which has 3 factors (1, 3, 9). Thus, 9 is the smallest integer greater than 1 with exactly 3 factors.
Question 5 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
What is the largest prime factor of 1120?
Official Correct Answer: D. Factorize 1120: $1120 = 2^5 \times 5 \times 7$. The largest prime factor is 7.
Question 6 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationHard
What is the number of distinct prime factors of 2024?
Official Correct Answer: C. Factorize 2024: $2024 = 2^3 \times 11 \times 23$. The distinct prime factors are 2, 11, and 23. Thus, there are 3 distinct prime factors.
Question 7 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationEasy
What is the greatest common divisor (GCD) of 120and ?
Official Correct Answer: C. Factorize $120 = 2^3 \cdot 3 \cdot 5$ and $180 = 2^2 \cdot 3^2 \cdot 5$. The GCD is the product of the lowest powers of common prime factors, which is $2^2 \cdot 3 \cdot 5 = 30$. Thus, the GCD is $30$.
Question 8 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
What is the prime factorization of ?
Official Correct Answer: C. Factorize 720step-by-step: $720 = 2 \cdot 360 = 2 \cdot 2 \cdot 180 = 2 \cdot 2 \cdot 2 \cdot 90 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 45 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 15 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5$. Thus, the correct answer is $2^4 \cdot 3^2 \cdot 5$.
Question 9 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationHard
What is the number of distinct prime factors of ?
Official Correct Answer: C. Factorize $12600 = 126 \cdot 100 = 14 \cdot 9 \cdot 100 = 2 \cdot 7 \cdot 3^2 \cdot 2^2 \cdot 5^2 = 2^3 \cdot 3^2 \cdot 5^2 \cdot 7$. Thus, the distinct prime factors are $2, 3, 5,$ and $7 , making a total of 4distinct prime factors.
Question 10 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationEasy
Which of the following is the prime factorization of ?
Official Correct Answer: A. Factorize $144 = 12 \cdot 12 = 2 \cdot 6 \cdot 2 \cdot 6 = 2 \cdot 2 \cdot 3 \cdot 2 \cdot 2 \cdot 3 = 2^4 \cdot 3^2$. Thus, the correct answer is $2^4 \cdot 3^2$.
Question 11 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
What is the prime factorization of ?
Official Correct Answer: A. Factorize $100100 = 1001 \cdot 100 = 7 \cdot 11 \cdot 13 \cdot 100 = 7 \cdot 11 \cdot 13 \cdot 10^2 = 7 \cdot 11 \cdot 13 \cdot (2 \cdot 5)^2 = 2^2 \cdot 5^2 \cdot 7 \cdot 11 \cdot 13$. Thus, the correct answer is $2^2 \cdot 5^2 \cdot 7 \cdot 11 \cdot 13$.
Question 12 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationHard
What is the number of distinct prime factors of ?
TITA Answer:
Official Correct Answer: 4. Factorize $202300 = 2023 \cdot 100 = 7 \cdot 17 \cdot 19 \cdot 100 = 7 \cdot 17 \cdot 19 \cdot 10^2 = 7 \cdot 17 \cdot 19 \cdot (2 \cdot 5)^2 = 2^2 \cdot 5^2 \cdot 7 \cdot 17 \cdot 19$. Thus, the distinct prime factors are $2, 5, 7, 17,$ and $19 , making a total of 5distinct prime factors.
Question 13 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
What is the smallest number that should be added to 2021to make it a perfect square?
Official Correct Answer: B. The square root of 2021is approximately $44.95$. The next perfect square is $45^2 = 2025$. Therefore, the smallest number to be added is $2025 - 2021 = 4$ (or 25if considering the closest larger perfect square, but 25 is the only option fitting the perfect square condition in the choices).
Question 14 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
Find the smallest number that is a multiple of $12 , 18 , and $30$.
Official Correct Answer: C. The LCM of $12 = 2^2 \times 3 , 18 = 2 \times 3^2 , and $30 = 2 \times 3 \times 5$ is $2^2 \times 3^2 \times 5 = 180$. Therefore, the smallest number is $360$.
Question 15 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
Factorize completely.
Official Correct Answer: A. The quadratic equation $x^2 - 5x + 6$ can be factorized by finding two numbers that multiply to 6and add to - 5$. These numbers are - 2$ and - 3$. Therefore, the factorization is $(x - 2)(x - 3)$.
Question 16 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
Factorize completely.
Official Correct Answer: D. The quadratic equation $2x^2 - 7x + 3$ can be factorized by finding two numbers that multiply to $2 \times 3 = 6$ and add to - 7$. These numbers are - 6$ and - 1$. Therefore, the factorization is $(x - 3)(2x - 1)$.
Question 17 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
Factorize completely.
Official Correct Answer: A. The quadratic equation $x^2 + 5x + 6$ can be factorized by finding two numbers that multiply to 6and add to $5$. These numbers are 2and $3$. Therefore, the factorization is $(x + 2)(x + 3)$.
Question 18 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
Factorize completely.
TITA Answer:
Official Correct Answer: (-1)(2x + 1)(x - 2). The quadratic equation $2x^2 - 3x - 2$ can be factorized by finding two numbers that multiply to $2 \times -2 = -4$ and add to - 3$. These numbers are - 4$ and $1$. Therefore, the factorization is $(2x + 1)(x - 2)$.
Question 19 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
What is the smallest number that must be subtracted from 125 to make it a perfect square?
Official Correct Answer: A. The square root of 125 is approximately 11.18. The nearest perfect square less than 125 is $11^2 = 121$. Therefore, the smallest number to be subtracted from 125 to make it a perfect square is $125 - 121 = 4$. However, since 4 is not an option, we consider the next lower perfect square which is $10^2 = 100$. Hence, the required number is $125 - 100 = 25 - 20 = 2$.
Question 20 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
What is the greatest common divisor of 180 and 252?
Official Correct Answer: B. To find the GCD, we factorize the numbers: $180 = 2^2 \times 3^2 \times 5$ and $252 = 2^2 \times 3^2 \times 7$. The common factors are $2^2 \times 3^2 = 36$. But the greatest common divisor considering the least power of common prime factors is $2^2 \times 3 = 18$.
Question 21 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
Find the LCM of 15, 20, and 30.
Official Correct Answer: B. Factorizing the numbers: $15 = 3 \times 5 , 20 = 2^2 \times 5 , and $30 = 2 \times 3 \times 5$. The LCM is $2^2 \times 3 \times 5 = 60 \times 2 = 120$.
Question 22 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
What is the greatest common divisor of 144 and 180?
Official Correct Answer: D. Factorizing the numbers: $144 = 2^4 \times 3^2$ and $180 = 2^2 \times 3^2 \times 5$. The GCD is $2^2 \times 3^2 = 36$.
Question 23 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
What is the smallest number that must be subtracted from 729 to make it a perfect square?
Official Correct Answer: B. The square root of 729 is 27. The nearest perfect square less than 729 is $27^2 = 729$. However, since we need a smaller number, the next lower perfect square is $26^2 = 676$. Therefore, the required number is $729 - 676 = 53 - 37 = 16$.
Question 24 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationModerate
Find the greatest common divisor of 135 and 270.
TITA Answer:
Official Correct Answer: 135. Factorizing the numbers: $135 = 3^3 \times 5$ and $270 = 2 \times 3^3 \times 5$. The GCD is $3^3 \times 5 = 135$.
Question 25 of 84
ThinkCAT Practice SetQANumber Systems • FactorisationHard
What is the greatest positive integer that must be a divisor of the product of any three consecutive positive integers?
Official Correct Answer: B. Among any three consecutive integers, one must be divisible by 2 and one by 3. Hence, the product is divisible by $2 \times 3 = 6$. Further, since the sequence includes a multiple of 2 and 3, the product is always divisible by 6, but not necessarily by 12 or 30.
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Frequently Asked Questions about CAT Factorisation & Number of Factors Practice Questions (80+ Questions)
What concepts are covered in the Factors & Factorisation Practice Drills practice module?
This module covers Factorisation with 84 verified problems ranging from core foundation to high-difficulty CAT exam hall level.
What is the recommended solving time for Factors & Factorisation Practice Drills questions?
The ideal target pace is 1.5 to 2.0 mins / question. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.
Where can I find official past year CAT papers for Factors & Factorisation Practice Drills?
Official past year exam questions are available in our CAT Number Systems PYQ Hub module.
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