Question

How many ways 630 can be write Product of two co-prime number​

Answer 1

Answer:

630 = 2*3*3*5*7

Number of prime factors = 4

Number of possible ways to write a number as product of two co prime numbers = $2^{n-1}$

Number of possible ways to write 630 as product of two co prime numbers = $2^{4-1}$ => 8

Hope it helps

Answer 2

630 can be written in 8 ways as product of two co-prime number​

Given:

• 630

To Find:

• Number of ways 630 can be written as Product of two co-prime number​

Solution:

• "Prime Factorization is finding prime numbers/factors which when multiplied together results in the original number"
• Prime number is a natural number which has only two factors one and number itself.  (e.g. , 2 , 3 , 5 , 7 .... )
• Coprime numbers are different numbers which have only 1 as a common factor

Step 1:

Prime Factorize 630

630 = 2 x 3 x 3 x 5 x 7

Step 2:

3  is only prime factor which repeats

Hence 630 can be rewritten as

630 = 2 x 9 x 5 x 7

Here Each factor is co prime with other factor

Step 3:

Can be written in exponent form

630 = 2¹ × 5¹ ×  7¹ × 9¹

Hence number of factor = (1 + 1)(1 + 1)(1 + 1)(1 + 1) = 16

Each Product need 2 factors Hence 16/2 = 8 ways to write

1 x 630

2 x 315

5 x  126

7  x 90

9  x  70

10 x 63

14 x 45

18  x 35

630 can be written in 8 ways as product of two co-prime number​