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21 May, 11:27

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

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  1. 21 May, 11:45
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    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
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