Find the greatest number that will divide 186, 321 and 402 so as to leave the same remainder in each case.
27
The greatest number leaving the same remainder divides the differences between the numbers exactly.
Differences: \(321-186=135\), \(402-321=81\), \(402-186=216\).
HCF of 135, 81 and 216: \(\text{HCF}(135,81)=27\), and \(\text{HCF}(27,216)=27\).
Hence, the greatest such number is 27.
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Important Questions from LCM and HCF
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Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Calculate the HCF of \(\frac{12}{5}\) , \(\frac{14}{15}\) and \(\frac{16}{17}\) .
Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 8280. What is their HCF?
