Highest Common Factor of 767, 565, 31 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 767, 565, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 767, 565, 31 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 767, 565, 31 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 767, 565, 31 is 1.

HCF(767, 565, 31) = 1

HCF of 767, 565, 31 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 767, 565, 31 is 1.

Highest Common Factor of 767,565,31 using Euclid's algorithm

Highest Common Factor of 767,565,31 is 1

Step 1: Since 767 > 565, we apply the division lemma to 767 and 565, to get

767 = 565 x 1 + 202

Step 2: Since the reminder 565 ≠ 0, we apply division lemma to 202 and 565, to get

565 = 202 x 2 + 161

Step 3: We consider the new divisor 202 and the new remainder 161, and apply the division lemma to get

202 = 161 x 1 + 41

We consider the new divisor 161 and the new remainder 41,and apply the division lemma to get

161 = 41 x 3 + 38

We consider the new divisor 41 and the new remainder 38,and apply the division lemma to get

41 = 38 x 1 + 3

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

38 = 3 x 12 + 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 767 and 565 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(38,3) = HCF(41,38) = HCF(161,41) = HCF(202,161) = HCF(565,202) = HCF(767,565) .

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

Step 1: Since 31 > 1, we apply the division lemma to 31 and 1, to get

31 = 1 x 31 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31 is 1

Notice that 1 = HCF(31,1) .

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Frequently Asked Questions on HCF of 767, 565, 31 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 767, 565, 31?

Answer: HCF of 767, 565, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 767, 565, 31 using Euclid's Algorithm?

Answer: For arbitrary numbers 767, 565, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.