What is the smallest number whose prime factorisation has : Class 6

What is the smallest number whose prime factorisation has : Class 6

Question 1.

What is the smallest number whose prime factorisation has : Class 6

(a) three different prime numbers?

(b) four different prime numbers?

Solution:

(a) This number is 2 × 3 × 5 = 30.

(b) This number is 2 × 3 × 5 × 7 = 210.

Question 2.

Are the following pairs of numbers co-prime? Guess first and then use prime factorisation to verify your answer. Class 6

(a) 30 and 45

(b) 57 and 85

(c) 121 and 1331

(d) 343 and 216

Solution:

(a) 30 = 2 × 3 × 5 and 45 = 3 × 3 × 5.

Since prime factors 3 and 5 are common in these numbers, so they are not co-prime.

(b) 57 = 3 × 19 and 85 = 5 × 17.

Since there is no common prime factor in these numbers, so they are co-prime.

(c) 121 = 11 × 11 and 1331 = 11 × 11 × 11.

Since, prime factor 11 and 11 are common

factors, so these numbers are not co-prime.

(d) 343 = 7 × 7 × 7 and 216 = 2 × 2 × 2 × 3 × 3 × 3.

Since there is no common prime factor in these numbers, so they are co-prime.