This set of Aptitude Questions and Answers (MCQs) focuses on “Factors and Sum of Factors”.
1. What is the number of factors of the number 9600?
a) 10
b) 48
c) 14
d) 44
View Answer
Explanation: The number 3600 can be factorized into, 9600 = 27 * 3 * 52.
Therefore, the total number of factors of 9600 is (7+1)*(1+1)*(2+1) = 48.
2. How many factors of 27 * 39 are perfect squares?
a) 80
b) 20
c) 40
d) 24
View Answer
Explanation: To find perfect square factors, we must express the number in the powers of perfect squares.
27 * 39 = 2 * 3 * 43 * 94.
Hence, the number of perfect square factors is (3+1)*(4+1) = 20.
3. How many 2-digit numbers are there which has only 3 factors (including 1)?
a) 2
b) 3
c) 6
d) 5
View Answer
Explanation: The numbers which have only 3 factors are squares of prime numbers.
25 and 49 are the only 2-digit squares of prime number 5 and 7.
Hence, there are only two 2-digit numbers are there which has only 3 factors (including 1).
4. How many prime factors are there in 2100?
a) 36
b) 6
c) 32
d) 12
View Answer
Explanation: The number 2100 can be factorized into, 2100 = 22*3*52*7.
Hence, the number of prime factors is 2+1+2+1 = 6.
5. How many distinct prime factors are there in 9900?
a) 4
b) 7
c) 54
d) 27
View Answer
Explanation: The number 9900 can be factorized into, 9900 =22*32*52*11.
Hence, there are 4 distinct prime factors i.e., 2, 3, 5 and 11.
6. Find the sum of all factors of 800.
a) 1953
b) 1835
c) 1623
d) 1756
View Answer
Explanation: 800 = 25*52.
The sum of all factors is given by (20 + 21 + 22 + 23 + 24 + 25)(50 + 51 + 52) = 63*31 = 1953.
7. Find the number of divisors of 711 which are greater than 4.
a) 5
b) 8
c) 6
d) 4
View Answer
Explanation: 711 = 32*79.
The number of factors of 711 is (2+1)(1+1) = 6.
There are 2 factors which are less than 4 i.e., 1 and 3.
Therefore, the number of divisors of 711 which are greater than 4 is 6-2 = 4.
8. Find the number of divisors of 616 excluding 1 and 616.
a) 16
b) 15
c) 14
d) 12
View Answer
Explanation: 616 = 23*7*11.
The number of factors of 616 is (3+1)(1+1)(1+1) = 16.
Therefore, the number of divisors of 616 excluding 1 and 616 is 14.
9. Find the number of factors of 1001, excluding the multiples of 1001.
a) 8
b) 7
c) 6
d) 5
View Answer
Explanation: 1001 = 7*11*13.
The number of factors of 1001 is (1+1)(1+1)(1+1) = 8.
There is only 1 multiple of 1001 i.e., 1001*1.
Therefore, the number of factors of 1001, excluding the multiples of 1001 is 7.
10. Find the number of factors of 693 excluding the multiples of 7.
a) 12
b) 9
c) 8
d) 6
View Answer
Explanation: 693 = 32*7*11.
The number of factors of 693 is (2+1)(1+1)(1+1) = 12.
The factors which are multiples of 7 are 7, 7*3, 7*9, 7*11, 7*3*11 and 7*9*11. So, there are 6 multiples of 7.
Therefore, the number of factors of 693 excluding the multiples of 7 is 12-6 = 6.
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