Highest Common Factor of 972, 302, 317 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, 302, 317 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 972, 302, 317 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, 302, 317 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, 302, 317 is 1.

HCF(972, 302, 317) = 1

HCF of 972, 302, 317 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, 302, 317 is 1.

Highest Common Factor of 972,302,317 using Euclid's algorithm

Highest Common Factor of 972,302,317 is 1

Step 1: Since 972 > 302, we apply the division lemma to 972 and 302, to get

972 = 302 x 3 + 66

Step 2: Since the reminder 302 ≠ 0, we apply division lemma to 66 and 302, to get

302 = 66 x 4 + 38

Step 3: We consider the new divisor 66 and the new remainder 38, and apply the division lemma to get

66 = 38 x 1 + 28

We consider the new divisor 38 and the new remainder 28,and apply the division lemma to get

38 = 28 x 1 + 10

We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get

28 = 10 x 2 + 8

We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get

10 = 8 x 1 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 972 and 302 is 2

Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(38,28) = HCF(66,38) = HCF(302,66) = HCF(972,302) .

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

Step 1: Since 317 > 2, we apply the division lemma to 317 and 2, to get

317 = 2 x 158 + 1

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

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 317 is 1

Notice that 1 = HCF(2,1) = HCF(317,2) .

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Frequently Asked Questions on HCF of 972, 302, 317 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, 302, 317?

Answer: HCF of 972, 302, 317 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 972, 302, 317 using Euclid's Algorithm?

Answer: For arbitrary numbers 972, 302, 317 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.