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
6 months, 2 weeks ago

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Hint: Let \(A\) and \(B\) be the 2 integers. Show that \(\dfrac A6\) and \( \dfrac B6\) are coprime.

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

Pi Han Goh - 6 months, 2 weeks ago

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

Erica Phillips - 6 months, 2 weeks ago

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

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

For example \( 1\times 420 \), \(4\times 105\), \(3\times35\), \(15 \times 7\).

Is there any other way?

Pi Han Goh - 6 months, 2 weeks 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 - 6 months, 2 weeks ago

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@Erica Phillips Both \(A\) and \(B\) are divisible by 6, right?

Are there any other larger integer that must divide both \(A\) and \(B\)?

Pi Han Goh - 6 months, 2 weeks ago

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@Pi Han Goh but why is it 6??

Erica Phillips - 6 months, 2 weeks 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 \(A\) and \(B\) is....?

Pi Han Goh - 6 months, 2 weeks ago

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@Pi Han Goh oh ok thanx !!

Erica Phillips - 6 months, 2 weeks ago

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

Erica Phillips - 6 months, 2 weeks ago

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@Erica Phillips No. \(\quad \quad \)

Pi Han Goh - 6 months, 2 weeks ago

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