Square root

hello , I really urgently need your help in this problem The product of 2 natural nos. is 15120 and their HCF is 6.Find how many such pairs exist.

Pls help me to find the solution to this problem

Note by Erica Phillips
1 year, 7 months ago

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Hint: Let AA and BB be the 2 integers. Show that A6\dfrac A6 and B6 \dfrac B6 are coprime.

Hint 2: Factorize 151206×6 \dfrac{15120}{6\times6} into product of 2 coprime posiitve integers.

Pi Han Goh - 1 year, 7 months ago

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I have factorized 420 by 7 and 5 and then??

erica phillips - 1 year, 7 months ago

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We know that A/6A/6 and B/6B/6 are coprime positive integers, and that A/6×B/6=420 A/6 \times B/6 = 420 .

So we want to find 2 coprime positive integers that give a product of 420.

For example 1×420 1\times 420 , 4×1054\times 105, 3×353\times35, 15×715 \times 7.

Is there any other way?

Pi Han Goh - 1 year, 7 months ago

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@Pi Han Goh I just wanna ask why have you divided A and B by 6 to prove that they are co prime??

erica phillips - 1 year, 7 months ago

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@Erica Phillips Both AA and BB are divisible by 6, right?

Are there any other larger integer that must divide both AA and BB?

Pi Han Goh - 1 year, 7 months ago

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@Pi Han Goh but why is it 6??

erica phillips - 1 year, 7 months ago

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@Erica Phillips Your question reads:

... The product of 2 natural nos. is 15120 and their HCF is 6

In other words, the largest integer that divides both AA and BB is....?

Pi Han Goh - 1 year, 7 months ago

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@Pi Han Goh oh ok thanx !!

erica phillips - 1 year, 7 months ago

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@Erica Phillips so u wanna say that 1420,4105,335,157 are the probable pairs.right??

erica phillips - 1 year, 7 months ago

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@Erica Phillips No. \quad \quad

Pi Han Goh - 1 year, 7 months ago

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