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The Euclidean algorithm is used to calculate the

This question was previously asked in
CDS I 2020 Elementary Mathematics Previous Year Paper (02-Feb-2020)
The correct answer is

HCF of two integers

The correct answer is HCF of two integers.

The Euclidean algorithm is a highly efficient method for computing the highest common factor (HCF) , also known as the greatest common divisor (GCD) , of two integers. It is one of the oldest algorithms known, dating back to ancient Greek mathematician Euclid's Elements. Therefore, the Euclidean algorithm is used to calculate the HCF of two integers.

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Similar Questions

  1. If (x + k) is the HCF of x 2+ px + q and x 2+ qx + p, where p ≠ q, then what is the value of k ?

  2. If (x + k) is the HCF of x 2+ 5x + 6 and x 2+ 8x + 15, then what is the value of k?

  3. Let L be the LCM and H be the HCF of two given numbers. L and H are in the ratio 3 ∶ 2. If the sum of the two numbers is 45, then what is the product of the numbers?

  4. A floor of a big hall has dimensions 30 m 60 cm and 23 m 40 cm. It is to be paved with square tiles of same size. What is the minimum number of tiles required ?

  5. The sum of LCM and HCF of two numbers is 1484 and the difference between LCM and HCF is. 1428. If one of the numbers is 112, then what is the other number?

  6. The LCM of two prime numbers p and q is 2231, where p > q. What is the value of p - q ?

  7. What is the HCF of (x8– y8) and (x7– y7+ x5y2– x2y5) ? 

  8. Three runners are running in a circular track, and they complete one round in 20, 30 and 35 minutes respectively. When will they next meet at the starting point ?

  9. What is the least perfect square which is divisible by 3, 4, 5, 6 and 7?

  10. If (x - k) is the HCF of x 2+ ax + b and x 2+ cx + d, then what is the value of k?


Important Questions from LCM and HCF

  1. 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:

  2. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.

  3. Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?

  4. The sum of two numbers is 1215 and their HCF is 81. How many such pairs of numbers can be formed?

  5. The LCM of two numbers in 48. Their ratio is 2:3 What is the sum of the numbers?

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