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The number of ordered pairs (a, b) of positive integers such that a + b = 90 and their greatest common divisor is 6 equals.
we have been given GCD of a and b = 6so we can say, a = 6x and b = 6ynow, a + b = 906x + 6y = 90x + y = 15x and y can be x = 1 then y = 14,x = 2 then y = 13x = 4 then y = 11x = 7 then y = 8ordered pair can be (6x, 6y),(6, 84) , (12, 78), (24, 66), ( 42, 48), (84,6), (78,12), (66, 24), (48, 42)there are total 8 ordered pair.
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