Highest Common Factor of 672, 913 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 672, 913 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 672, 913 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 672, 913 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 672, 913 is 1.

HCF(672, 913) = 1

HCF of 672, 913 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 672, 913 is 1.

Highest Common Factor of 672,913 using Euclid's algorithm

Highest Common Factor of 672,913 is 1

Step 1: Since 913 > 672, we apply the division lemma to 913 and 672, to get

913 = 672 x 1 + 241

Step 2: Since the reminder 672 ≠ 0, we apply division lemma to 241 and 672, to get

672 = 241 x 2 + 190

Step 3: We consider the new divisor 241 and the new remainder 190, and apply the division lemma to get

241 = 190 x 1 + 51

We consider the new divisor 190 and the new remainder 51,and apply the division lemma to get

190 = 51 x 3 + 37

We consider the new divisor 51 and the new remainder 37,and apply the division lemma to get

51 = 37 x 1 + 14

We consider the new divisor 37 and the new remainder 14,and apply the division lemma to get

37 = 14 x 2 + 9

We consider the new divisor 14 and the new remainder 9,and apply the division lemma to get

14 = 9 x 1 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma 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 672 and 913 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(14,9) = HCF(37,14) = HCF(51,37) = HCF(190,51) = HCF(241,190) = HCF(672,241) = HCF(913,672) .

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Frequently Asked Questions on HCF of 672, 913 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 672, 913?

Answer: HCF of 672, 913 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 672, 913 using Euclid's Algorithm?

Answer: For arbitrary numbers 672, 913 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.