# Find the g.c.d of 15 and 28 .

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To find the greatest common divisor we first expresses the numbers the the products of their prime factors. Then the factors which are common in all the three sets of prime factors are taken and multiplied to arrive at the GCD.

15 can be written as 5 * 3

28 is 7 * 2* 2

Therefore there are no common factors between the two, so the GCD is equal to 1.

**The required GCD is 1.**

To get the greatest common divisor of 15 and 28.

Solution :

We write both 15 and 28 with their prime factor in their highest power:

15 = 1*3*5............(1)

28 = 1*2*2*7 = 2^2 *7...........(2)

We examine the factors of 15 and 28 at the RHS of (1) and (2).

There are no common factors between 15 and 28 except 1.

Therefore 1 is the onl common factor for 15 and 28.

Therefore the GCD or GCF of 15 and 28 is 1.

To calculate the greatest common divisor of 15 and 28, we'll factor 15 and 28 into their prime factors.

15 = 3*5

18 = 2*2*7

Now, we'll consider the common factors from both numbers and we'll multiply them.

We notice that the numbers don't have other common factors besides 1.

So the greatest common divisor is1.

**gcd {15 , 28} = 1**

**If 2 numbers have the gcd = 1 they are relatively prime, so 15 and 28 are relatively prime.**