Highest Common Factor of 972, 620, 217 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 972, 620, 217 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 972, 620, 217 is 1 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 972, 620, 217 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 972, 620, 217 is 1.

HCF(972, 620, 217) = 1

HCF of 972, 620, 217 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 972, 620, 217 is 1.

Highest Common Factor of 972,620,217 using Euclid's algorithm

Highest Common Factor of 972,620,217 is 1

Step 1: Since 972 > 620, we apply the division lemma to 972 and 620, to get

972 = 620 x 1 + 352

Step 2: Since the reminder 620 ≠ 0, we apply division lemma to 352 and 620, to get

620 = 352 x 1 + 268

Step 3: We consider the new divisor 352 and the new remainder 268, and apply the division lemma to get

352 = 268 x 1 + 84

We consider the new divisor 268 and the new remainder 84,and apply the division lemma to get

268 = 84 x 3 + 16

We consider the new divisor 84 and the new remainder 16,and apply the division lemma to get

84 = 16 x 5 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 972 and 620 is 4

Notice that 4 = HCF(16,4) = HCF(84,16) = HCF(268,84) = HCF(352,268) = HCF(620,352) = HCF(972,620) .

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

Step 1: Since 217 > 4, we apply the division lemma to 217 and 4, to get

217 = 4 x 54 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 217 is 1

Notice that 1 = HCF(4,1) = HCF(217,4) .

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Frequently Asked Questions on HCF of 972, 620, 217 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 972, 620, 217?

Answer: HCF of 972, 620, 217 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 972, 620, 217 using Euclid's Algorithm?

Answer: For arbitrary numbers 972, 620, 217 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.