Highest Common Factor of 84, 972, 638 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 84, 972, 638 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 84, 972, 638 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 84, 972, 638 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 84, 972, 638 is 2.

HCF(84, 972, 638) = 2

HCF of 84, 972, 638 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 84, 972, 638 is 2.

Highest Common Factor of 84,972,638 using Euclid's algorithm

Highest Common Factor of 84,972,638 is 2

Step 1: Since 972 > 84, we apply the division lemma to 972 and 84, to get

972 = 84 x 11 + 48

Step 2: Since the reminder 84 ≠ 0, we apply division lemma to 48 and 84, to get

84 = 48 x 1 + 36

Step 3: We consider the new divisor 48 and the new remainder 36, and apply the division lemma to get

48 = 36 x 1 + 12

We consider the new divisor 36 and the new remainder 12, and apply the division lemma to get

36 = 12 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 84 and 972 is 12

Notice that 12 = HCF(36,12) = HCF(48,36) = HCF(84,48) = HCF(972,84) .


We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 638 > 12, we apply the division lemma to 638 and 12, to get

638 = 12 x 53 + 2

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 2 and 12, to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 12 and 638 is 2

Notice that 2 = HCF(12,2) = HCF(638,12) .

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Frequently Asked Questions on HCF of 84, 972, 638 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 84, 972, 638?

Answer: HCF of 84, 972, 638 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 84, 972, 638 using Euclid's Algorithm?

Answer: For arbitrary numbers 84, 972, 638 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.