**Quantitative Aptitude Practice questions on Number Systems - Factors**: This practice set has 12 questions with their answers & Explanatory answer covering topics from the areas of Quantitative Aptitude.

**1. The sum of the factors of a number is 124. What is the number?**

A. Number lies between 40 and 50

B. Number lies between 50 and 60

C. Number lies between 60 and 80

D. More than one such number exists

**2. How many factors of 1080 are perfect squares?**

A. 4

B. 6

C. 8

D. 5

**3. How many factors of 2 ^{5} * 3^{6} * 5^{2} are perfect squares?**

A. 18

B. 24

C. 36

D. 8

**4. How many factors of 2 ^{4} * 5^{3} * 7^{4} are odd numbers?**

A. 100

B. 99

C. 20

D. 24

**5. How many factors of the number 2 ^{8} * 3^{6} * 5^{4} * 10^{5} are multiples of 120?**

A. 540

B. 660

C. 594

D. 792

**6. Number N = 2 ^{6} * 5^{5} * 7^{6} * 10^{7}; how many factors of N are even numbers?**

A. 1183

B. 1200

C. 1050

D. 840

**7. Numbers A, B, C and D have 16, 28, 30 and 27 factors. Which of these could be a perfect cube?**

A. A and B

B. B and C

C. A, B and C

D. B and D

**8. If a three digit number ‘abc’ has 3 factors, how many factors does the 6-digit number ‘abcabc’ have?**

A. 16 factors

B. 24 factors

C. 16 or 24 factors

D. 20 factors

**9. How many numbers are there less than 100 that cannot be written as a multiple of a perfect square greater than 1?**

A. 61

B. 56

C. 52

D. 65

**10. Find the smallest number that has exactly 18 factors.**

A. 180

B. 216

C. 240

D. None of these

**11. A number N ^{2} has 15 factors. How many factors can N have?**

A. 5 or 7 factors

B. 6 or 8 factors

C. 4 or 6 factors

D. 9 or 8 factors

**12. If a three digit number ‘abc’ has 2 factors (where a, b, c are digits), how many factors does the 6-digit number ‘abcabc’ have?**

A. 16

B. 24

C. 18

D. 30

**Answer Key –**

Q.No. | 1. | 2. | 3. | 4. | 5. | 6. | 7. | 8. | 9. | 10. | 11. | 12. |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Ans. | (D) | (A) | (B) | (C) | (C) | (A) | (A) | (C) | (A) | (A) | (B) | (A) |

**Solution Link -** http://iim-cat-questions-answers.2iim.com/quant/number-system/factors/