Quantitative Aptitude ยท Mathematics

Numbers and Divisibility

215 Questions

Master the number system by solving these quantitative aptitude questions on divisibility rules and properties. The exercises cover finding the greatest common divisor and identifying prime factors. This topic is essential for clearing the preliminary stages of SSC, banking, and various state exams.

Divisibility rulesGreatest common divisorPolynomial divisionNatural numbersFactorizationPrime numbers

Numbers and Divisibility Questions

Multiple choice

What is the greatest common divisor (GCD) of 18 and 24?

  1. 2

  2. 3

  3. 6

  4. 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The GCD of 18 and 24 can be found using the Euclidean algorithm: 24 = 18 * 1 + 6; 18 = 6 * 3 + 0. Therefore, the GCD is 6.

Multiple choice

Find the smallest positive integer n such that n! is divisible by 100.

  1. 15

  2. 20

  3. 25

  4. 30
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To be divisible by 100, n! must contain at least two factors of 5. The smallest positive integer that satisfies this condition is 25, as 25! contains two factors of 5.

Multiple choice

What is the sum of all the positive integers less than 100 that are divisible by 7?

  1. 700

  2. 770

  3. 840

  4. 910
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The multiples of 7 less than 100 are: 7, 14, 21, ..., 98. The sum of this arithmetic sequence can be calculated using the formula: sum = (n/2) * (a1 + an), where n is the number of terms, a1 is the first term, and an is the last term. Plugging in the values, we get: sum = (14/2) * (7 + 98) = 840.

Multiple choice

Find the number of positive integers less than 1000 that are divisible by 3 but not by 5.

  1. 166

  2. 200

  3. 266

  4. 332
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To be divisible by 3 but not by 5, a number must be divisible by 3 but not divisible by 15. The multiples of 3 less than 1000 are: 3, 6, 9, ..., 999. The multiples of 15 less than 1000 are: 15, 30, 45, ..., 990. Subtracting the multiples of 15 from the multiples of 3, we get the numbers that are divisible by 3 but not by 5. There are 266 such numbers.

Multiple choice

Find the greatest common divisor (GCD) of 24 and 36 using the Euclidean algorithm.

  1. 6

  2. 8

  3. 12

  4. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the Euclidean algorithm, we have: 36 = 24 * 1 + 12, 24 = 12 * 2 + 0. Therefore, the GCD of 24 and 36 is 12.