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(#M40010578) SELF question Keep an EYE

The sum of a pair of positive integers is 336 and the H.C.F. is 21. The number of such possible pairs is :

Arjun (12 years ago)

Solved Garima Read Solution (5)

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Meena  (12 years ago)

The sum of a pair of positive integers is 336 and the H.C.F. is 21.

It means numbers are 21x and 21 y where x and y are relatively prime ( no common factor).
21x+21y = 336
x+y = 336/21 = 16
possible value of x,y are
1,15
3,13,
5,11,
7,9

so 4 pairs are possible.
If u consider interchanging values of x and y, u can consider as 8 pairs.

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Garima  (12 years ago)

4 pairs

(21,315), (63,273), (105,231), (147,189)

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chandra  (11 years ago)

there are 8 possible values
(21,315)
(42,294)
(63,273)
(84,252)
(105,231)
126,210)
(147,189)
(168,168)

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Chirag Ranjan Lahiri  (10 years ago)

4 pairs

(21,315), (63,273), (105,231), (147,189)

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tonynash  (8 years ago)

WE HAVE TO CONSIDER PRIME NUMBER PAIRS...HENCE 4 IS THE ANSWER..IF WE CONSIDER 2,14 i.e 42,294 HCF WILL DIFFER

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