The greatest number, which divides 711 and 1040 to leave 48 and 20 respectively as remainders, is:
Given:
First number = 711, Remainder = 48
Second number = 1040, Remainder = 20
Formula Used:
If a number leaves remainders r₁ and r₂ on dividing numbers a and b, then
Greatest required number = HCF(a − r₁, b − r₂)
Solution:
Subtract the remainders from the given numbers:
711 − 48 = 663
1040 − 20 = 1020
Now find the HCF of 663 and 1020:
1020 = 663 × 1 + 357
663 = 357 × 1 + 306
357 = 306 × 1 + 51
306 = 51 × 6 + 0
Hence,
HCF(663, 1020) = 51
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