A number for which the sum of all its factors is equal to twice the number is called a _____ number.

The number of common prime factors of 75, 60, and 105 is

A number is divisible by 5 and 6. It may not be divisible by

Express each of the following numbers as the sum of three odd primes:

(a) 21 (b) 31

(c) 53 (d) 61

In which of the following expressions, prime factorisation has been done?

(a) 24 = 2 × 3 × 4

(b) 56 = 7 × 2 × 2 × 2

(c) 70 = 2 × 5 × 7

(d) 54 = 2 × 3 × 9

Find all the prime factors of 1729 and arrange them in ascending order. Now state the relation, if any; between two consecutive prime factors.

Find first three common multiples of:

(a) 6 and 8 (b) 12 and 18

Which of the following statements are true?

(a) If a number is divisible by 3, it must be divisible by 9.

(b) If a number isd divisible by 9, it must be divisible by 3.

(c) A number is divisible by 18, if it is divisible by both 3 and 6.

(d) If a number is divisible by 9 and 10 both, then it must be divisible by 90.

(e) If two numbers are co-prime, at least one of them must be prime.

(f) All numbers which are divisible by 4 must also be divisible by 8.

(g) All numbers which are divisible by 8 must also be divisible by 4.

(h) If a number exactly divides two numbers separately, it must exactly divide their su,

(i) If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

I am the smallest number, having four different prime factors. Can you find me?

Write five pairs of prime numbers below 20 whose sum is divisible by 5.

A number for which the sum of all its factors is equal to twice the number is called a _____ number.