Question

The product of two numbers is 4107. If the H.C.F. of these numbers is 37, then find the greater number.
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Answer 1

Let the numbers be 37a and 37b.
Then, 37a $\times$ 37b = 4107
ab = 3
Now, co-primes with product 3 are (1, 3).
So, the required numbers are $(37\times 1,37\times 3)$ i.e., (37, 111).
Greater number = 111.