Highest Common Factor of 767, 473, 692 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, 473, 692 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 767, 473, 692 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, 473, 692 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, 473, 692 is 1.

HCF(767, 473, 692) = 1

HCF of 767, 473, 692 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, 473, 692 is 1.

Highest Common Factor of 767,473,692 using Euclid's algorithm

Highest Common Factor of 767,473,692 is 1

Step 1: Since 767 > 473, we apply the division lemma to 767 and 473, to get

767 = 473 x 1 + 294

Step 2: Since the reminder 473 ≠ 0, we apply division lemma to 294 and 473, to get

473 = 294 x 1 + 179

Step 3: We consider the new divisor 294 and the new remainder 179, and apply the division lemma to get

294 = 179 x 1 + 115

We consider the new divisor 179 and the new remainder 115,and apply the division lemma to get

179 = 115 x 1 + 64

We consider the new divisor 115 and the new remainder 64,and apply the division lemma to get

115 = 64 x 1 + 51

We consider the new divisor 64 and the new remainder 51,and apply the division lemma to get

64 = 51 x 1 + 13

We consider the new divisor 51 and the new remainder 13,and apply the division lemma to get

51 = 13 x 3 + 12

We consider the new divisor 13 and the new remainder 12,and apply the division lemma to get

13 = 12 x 1 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 767 and 473 is 1

Notice that 1 = HCF(12,1) = HCF(13,12) = HCF(51,13) = HCF(64,51) = HCF(115,64) = HCF(179,115) = HCF(294,179) = HCF(473,294) = HCF(767,473) .

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

Step 1: Since 692 > 1, we apply the division lemma to 692 and 1, to get

692 = 1 x 692 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 692 is 1

Notice that 1 = HCF(692,1) .

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Frequently Asked Questions on HCF of 767, 473, 692 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, 473, 692?

Answer: HCF of 767, 473, 692 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 767, 473, 692 using Euclid's Algorithm?

Answer: For arbitrary numbers 767, 473, 692 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.