Highest Common Factor of 7972, 2173 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 7972, 2173 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7972, 2173 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 7972, 2173 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 7972, 2173 is 1.

HCF(7972, 2173) = 1

HCF of 7972, 2173 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 7972, 2173 is 1.

Highest Common Factor of 7972,2173 using Euclid's algorithm

Highest Common Factor of 7972,2173 is 1

Step 1: Since 7972 > 2173, we apply the division lemma to 7972 and 2173, to get

7972 = 2173 x 3 + 1453

Step 2: Since the reminder 2173 ≠ 0, we apply division lemma to 1453 and 2173, to get

2173 = 1453 x 1 + 720

Step 3: We consider the new divisor 1453 and the new remainder 720, and apply the division lemma to get

1453 = 720 x 2 + 13

We consider the new divisor 720 and the new remainder 13,and apply the division lemma to get

720 = 13 x 55 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 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 7972 and 2173 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(720,13) = HCF(1453,720) = HCF(2173,1453) = HCF(7972,2173) .

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Frequently Asked Questions on HCF of 7972, 2173 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 7972, 2173?

Answer: HCF of 7972, 2173 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7972, 2173 using Euclid's Algorithm?

Answer: For arbitrary numbers 7972, 2173 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.