CAT MCQs on Divisibility and Factors: CAT Questions for Practice with Solutions

Content Writer | MBA Professional | Updated on - Nov 26, 2025

The CAT QA section requires speed and accuracy, along with a thorough understanding of the Divisibility and Factors. This article provides a set of MCQs on Divisibility and Factors to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation

Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.

The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.

CAT MCQs on Divisibility and Factors

1. Let $n$ be the least positive integer such that $168$ is a factor of $1134^n$ . If $m$ is the least positive integer such that $1134^n$ is a factor of $168^m$ , then $m+ n $ equals

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2. The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

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3. How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

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4. Find the minimum integral value of n such that the division $55n/124$ leaves no remainder.

124

123

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5. If x is a positive integer such that 2x + 12 is divisible by x, then the number of possible values of x is:

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6. A man walks one km east, two km north, one km east, one km north, one km east, one km north. What is the shortest distance from the starting point to the destination?

$2\sqrt{2}$ km

7 km

$3\sqrt{2}$ km

5 km

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7. A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then $(p^2 - 1)$ is:

never divisible by 6

always divisible by 6, and may or may not be divisible by 12

always divisible by 12, and may or may not be divisible by 24

always divisible by 24

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8. To decide whether an n-digit number is divisible by 7, a process is defined by using weights of powers of 3 from the right: i.e., for number abc, compute $a \cdot 3^2 + b \cdot 3^1 + c \cdot 3^0$ Given: $259 \Rightarrow 2 \cdot 9 + 5 \cdot 3 + 9 = 18 + 15 + 9 = 42$ Now for number 203, how many such stages are needed to reduce it to 7?

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CAT Questions

1.
To decide whether an $n$-digit number is divisible by 7, a process is defined by using weights of powers of 3 from the right: i.e., for number $abc$, compute $a \cdot 3^2 + b \cdot 3^1 + c \cdot 3^0$ Given: $259 \Rightarrow 2 \cdot 9 + 5 \cdot 3 + 9 = 18 + 15 + 9 = 42$ Now for number 203, how many such stages are needed to reduce it to 7?

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2.
The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

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3.
If $x$ is a positive integer such that $2x + 12$ is divisible by $x$, then the number of possible values of $x$ is:

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4.
Let $n$ be the least positive integer such that $168$ is a factor of $1134^n$ . If $m$ is the least positive integer such that $1134^n$ is a factor of $168^m$ , then $m+ n $ equals

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5.
How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

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6.
For some natural number n,assume that $(15,000)!$ is divisible by $(n!)!$ The largest possible value of n is

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Categories	State
General	2400
sc	1200
pwd	1200

CAT MCQs on Divisibility and Factors: CAT Questions for Practice with Solutions

CAT MCQs on Divisibility and Factors

CAT Questions

2.
The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

3.
If $x$ is a positive integer such that $2x + 12$ is divisible by $x$, then the number of possible values of $x$ is:

4.
Let \(n\) be the least positive integer such that \(168\) is a factor of \(1134^n\) . If \(m\) is the least positive integer such that \(1134^n\) is a factor of \(168^m\) , then \(m+ n \) equals

5.
How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

6.
For some natural number n,assume that \((15,000)!\) is divisible by \((n!)!\) The largest possible value of n is

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CAT MCQs on Divisibility and Factors

CAT Questions

2.The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

3.If $x$ is a positive integer such that $2x + 12$ is divisible by $x$, then the number of possible values of $x$ is:

4.Let \(n\) be the least positive integer such that \(168\) is a factor of \(1134^n\) . If \(m\) is the least positive integer such that \(1134^n\) is a factor of \(168^m\) , then \(m+ n \) equals

5.How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

6.For some natural number n,assume that \((15,000)!\) is divisible by \((n!)!\) The largest possible value of n is

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2.
The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

3.
If $x$ is a positive integer such that $2x + 12$ is divisible by $x$, then the number of possible values of $x$ is:

4.
Let \(n\) be the least positive integer such that \(168\) is a factor of \(1134^n\) . If \(m\) is the least positive integer such that \(1134^n\) is a factor of \(168^m\) , then \(m+ n \) equals

5.
How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

6.
For some natural number n,assume that \((15,000)!\) is divisible by \((n!)!\) The largest possible value of n is