Highest Common Factor of 138, 417 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, 417 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 138, 417 is 3 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, 417 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, 417 is 3.

HCF(138, 417) = 3

HCF of 138, 417 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, 417 is 3.

Highest Common Factor of 138,417 using Euclid's algorithm

Highest Common Factor of 138,417 is 3

Step 1: Since 417 > 138, we apply the division lemma to 417 and 138, to get

417 = 138 x 3 + 3

Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 3 and 138, to get

138 = 3 x 46 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 138 and 417 is 3

Notice that 3 = HCF(138,3) = HCF(417,138) .

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Frequently Asked Questions on HCF of 138, 417 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, 417?

Answer: HCF of 138, 417 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 138, 417 using Euclid's Algorithm?

Answer: For arbitrary numbers 138, 417 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.