Which paire of numbers are reletavly prime A) 26 and 99, B) 90 and 117, C) 100 and 202, D) 201 and 444

Option A

26 and 99 are relatively prime numbers

Solution:

Let us first understand about relative prime numbers

Two integers a and b are said to be relatively prime, mutually prime, or co prime if the only positive integer (factor) that divides both of them is 1

Let us check the options

Option A

26 and 99

The factors of 26 = 1, 2, 13, 26

The factors of 99 = 1, 3, 9, 11, 33, 99

Thus there no common factors other than 1

So 26 and 99 are relatively prime numbers

Option B

90 and 117

The factors of 90 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

The factors of 117 = 1, 3, 9, 13, 39, 117

Here 3 and 9 are common factors

So 90 and 117 are not relative prime numbers

Option C

100 and 202

The factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100

The factors of 202 = 1, 2, 101, 202

Here 2 is a common factor

So 100 and 202 are not relative prime numbers

Option D

201 and 444

The factors of 201 = 1, 3, 67, 201

The factors of 444 = 1, 2, 3, 4, 6, 12, 37, 74, 111, 148, 222, 444

Here 3 is common factor

So 201 and 444 are not relative prime numbers