The sum of two positive integer is 594.The h.C.F is 33.The number of pairs of such numbers satisingfy these condiions?T
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Hi,
Let us consider, P and Q are the numbers whose HCF is H, then ,H should divide both P and Q.
P = H*p,
Q = H*q.
where p,q are integers prime to each other.
P = 33p, Q =33q
P+Q = 33p+33q = 33 (p+q) = 528
Thus (p+q) = 16.
Now we need to find the set of values of p&q such that they are positive co-prime and have their sum as 16.
thus, (p,q) = (1,5) ; (3,13) ; (5,11) ; (7,9)
Four pairs of such numbers are possible (33,495); (99,429); (165,363) & (231,297)
hope it helps u
Let us consider, P and Q are the numbers whose HCF is H, then ,H should divide both P and Q.
P = H*p,
Q = H*q.
where p,q are integers prime to each other.
P = 33p, Q =33q
P+Q = 33p+33q = 33 (p+q) = 528
Thus (p+q) = 16.
Now we need to find the set of values of p&q such that they are positive co-prime and have their sum as 16.
thus, (p,q) = (1,5) ; (3,13) ; (5,11) ; (7,9)
Four pairs of such numbers are possible (33,495); (99,429); (165,363) & (231,297)
hope it helps u
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