The prime factorisation of a number has one 2, two 3s, and one 11. What is the number? Class 6

The prime factorisation of a number has one 2, two 3s, and one 11. What is the number? Class 6

Question 1.

The prime factorisation of a number has one 2, two 3s, and one 11. What is the number? Class 6

Solution:

Required number = 2 × 3 × 3 × 11 = 198.

Question 2.

Find three prime numbers, all less than 30, whose product is 1955. Class 6

Solution:

1955 = 5 × 17 × 23. Thus, numbers are 5, 17 and 23.

Question 3.

Find the prime factorisation of these numbers without multiplying first Class 6

(a) 56 × 25

(b) 108 × 75

(c) 1000 × 81

Solution:

(a) 56 × 25 = 2 × 2 × 2 × 7 × 5 × 5 = 2 × 2 × 2 × 5 × 5 × 7;

(b) 108 × 75 = 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5 = 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5;

(c) 1000 × 81 = 2 × 2 × 2 × 5 × 5 × 5 × 3 × 3 × 3 × 3 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5 × 5.