Highest Common Factor of 138, 621 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 138, 621 i.e. 69 the largest integer that leaves a remainder zero for all numbers.

HCF of 138, 621 is 69 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 138, 621 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 138, 621 is 69.

HCF(138, 621) = 69

HCF of 138, 621 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 138, 621 is 69.

Highest Common Factor of 138,621 using Euclid's algorithm

Highest Common Factor of 138,621 is 69

Step 1: Since 621 > 138, we apply the division lemma to 621 and 138, to get

621 = 138 x 4 + 69

Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 69 and 138, to get

138 = 69 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 69, the HCF of 138 and 621 is 69

Notice that 69 = HCF(138,69) = HCF(621,138) .

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Frequently Asked Questions on HCF of 138, 621 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 138, 621?

Answer: HCF of 138, 621 is 69 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 138, 621 using Euclid's Algorithm?

Answer: For arbitrary numbers 138, 621 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.