Highest Common Factor of 972, 1307 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, 1307 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 972, 1307 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, 1307 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, 1307 is 1.

HCF(972, 1307) = 1

HCF of 972, 1307 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 972, 1307 is 1.

Highest Common Factor of 972,1307 using Euclid's algorithm

Highest Common Factor of 972,1307 is 1

Step 1: Since 1307 > 972, we apply the division lemma to 1307 and 972, to get

1307 = 972 x 1 + 335

Step 2: Since the reminder 972 ≠ 0, we apply division lemma to 335 and 972, to get

972 = 335 x 2 + 302

Step 3: We consider the new divisor 335 and the new remainder 302, and apply the division lemma to get

335 = 302 x 1 + 33

We consider the new divisor 302 and the new remainder 33,and apply the division lemma to get

302 = 33 x 9 + 5

We consider the new divisor 33 and the new remainder 5,and apply the division lemma to get

33 = 5 x 6 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 972 and 1307 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(33,5) = HCF(302,33) = HCF(335,302) = HCF(972,335) = HCF(1307,972) .

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Frequently Asked Questions on HCF of 972, 1307 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, 1307?

Answer: HCF of 972, 1307 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 972, 1307 using Euclid's Algorithm?

Answer: For arbitrary numbers 972, 1307 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.