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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.

The number of ordered pairs (a, b) of positive integers such that a + b = 90 and their greatest
common divisor is 6 equals.

Grade:10

1 Answers

Kriti Singh
askIITians Faculty 16 Points
2 years ago
we have been given GCD of a and b = 6
so we can say, a = 6x and b = 6y
now, a + b = 90
6x + 6y = 90
x + y = 15
x and y can be x = 1 then y = 14,
x = 2 then y = 13
x = 4 then y = 11
x = 7 then y = 8
ordered 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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