Prime Time Class 6 Short Question Answer

Prime Time Class 6 Short Question Answer

Prime Time Class 6 Short Question Answer

Question 1.

Find the greatest common factor of the numbers 70,105 and 175.

Solution:

Factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70; factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105 and factors of 175 are 1, 5, 7, 25, 35, 175.

Here, common factors are 5, 7 and 35, of these three, 35 is the greatest common factor.

Question 2.

Find the first common multiple of 18, 24 and 36.

Solution:

Multiple of 18 are 18, 36, 54, 72, 90, 108, 126, 144,...;

multiples of 24 are 24, 48, 72, 96, 120, 144,...;

multiples of 36 are 36, 72,108, 144, ...

Here, common multiples are 72, 144, ...

So, first common multiple is 72.

Question 3.

Using prime factorisation, check whether the numbers 1715 and 432 are co¬prime or not.

Solution:

Prime factorisation of 1715 = 5 × 7 × 7 × 7 and prime factorisation of 432 = 2 × 2 × 2 × 2 × 3 × 3 × 3.

As there is no common prime factor in the above two factorisation, so, the given numbers are co-prime.

Question 4.

Using prime factorisation, check whether 450 is divisible by 54.

Solution:

450 = 2 × 3 × 3 × 5 × 5 and 54 = 2 × 3 × 3 × 3. Since all the prime factors 2, 3, 3 and 3 of 54 are not included in the prime factors 2, 3, 3, 5 and 5 of 450, so 450 is not divisible by 54.

Question 5.

Write the prime factorisation of the product 216 x 150 without multiplying the numbers.

Solution:

We have :

216 × 150

= 2 × 2 × 2 × 3 × 3 × 3 × 2 × 3 × 5 × 5

= 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5