The product of two numbers and their HCF are 4107 and 37 respectively. Find the numbers.
37, 111
37, 111 is correct.
Since the HCF is 37, write the numbers as \(37a\) and \(37b\), where \(a\) and \(b\) have no common factor.
Their product is \(37a\times37b = 1369ab = 4107\), so \(ab = \dfrac{4107}{1369} = 3\).
The only co-prime pair with product 3 is \(a=1, b=3\), giving the numbers \(37\) and \(37\times3=111\).
Check: \(37\times111=4107\) and the HCF of 37 and 111 is 37. So the numbers are 37 and 111.
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Important Questions from LCM and HCF
The HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
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What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
