Highest Common Factor of 96, 731 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 96, 731 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 96, 731 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 96, 731 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 96, 731 is 1.

HCF(96, 731) = 1

HCF of 96, 731 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 96, 731 is 1.

Highest Common Factor of 96,731 using Euclid's algorithm

Highest Common Factor of 96,731 is 1

Step 1: Since 731 > 96, we apply the division lemma to 731 and 96, to get

731 = 96 x 7 + 59

Step 2: Since the reminder 96 ≠ 0, we apply division lemma to 59 and 96, to get

96 = 59 x 1 + 37

Step 3: We consider the new divisor 59 and the new remainder 37, and apply the division lemma to get

59 = 37 x 1 + 22

We consider the new divisor 37 and the new remainder 22,and apply the division lemma to get

37 = 22 x 1 + 15

We consider the new divisor 22 and the new remainder 15,and apply the division lemma to get

22 = 15 x 1 + 7

We consider the new divisor 15 and the new remainder 7,and apply the division lemma to get

15 = 7 x 2 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 96 and 731 is 1

Notice that 1 = HCF(7,1) = HCF(15,7) = HCF(22,15) = HCF(37,22) = HCF(59,37) = HCF(96,59) = HCF(731,96) .

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Frequently Asked Questions on HCF of 96, 731 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 96, 731?

Answer: HCF of 96, 731 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 96, 731 using Euclid's Algorithm?

Answer: For arbitrary numbers 96, 731 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.