Highest Common Factor of 938, 872 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 938, 872 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 938, 872 is 2 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 938, 872 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 938, 872 is 2.

HCF(938, 872) = 2

HCF of 938, 872 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 938, 872 is 2.

Highest Common Factor of 938,872 using Euclid's algorithm

Highest Common Factor of 938,872 is 2

Step 1: Since 938 > 872, we apply the division lemma to 938 and 872, to get

938 = 872 x 1 + 66

Step 2: Since the reminder 872 ≠ 0, we apply division lemma to 66 and 872, to get

872 = 66 x 13 + 14

Step 3: We consider the new divisor 66 and the new remainder 14, and apply the division lemma to get

66 = 14 x 4 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 938 and 872 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(66,14) = HCF(872,66) = HCF(938,872) .

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Frequently Asked Questions on HCF of 938, 872 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 938, 872?

Answer: HCF of 938, 872 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 938, 872 using Euclid's Algorithm?

Answer: For arbitrary numbers 938, 872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.