Highest Common Factor of 767, 442 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, 442 i.e. 13 the largest integer that leaves a remainder zero for all numbers.

HCF of 767, 442 is 13 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, 442 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, 442 is 13.

HCF(767, 442) = 13

HCF of 767, 442 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, 442 is 13.

Highest Common Factor of 767,442 using Euclid's algorithm

Highest Common Factor of 767,442 is 13

Step 1: Since 767 > 442, we apply the division lemma to 767 and 442, to get

767 = 442 x 1 + 325

Step 2: Since the reminder 442 ≠ 0, we apply division lemma to 325 and 442, to get

442 = 325 x 1 + 117

Step 3: We consider the new divisor 325 and the new remainder 117, and apply the division lemma to get

325 = 117 x 2 + 91

We consider the new divisor 117 and the new remainder 91,and apply the division lemma to get

117 = 91 x 1 + 26

We consider the new divisor 91 and the new remainder 26,and apply the division lemma to get

91 = 26 x 3 + 13

We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 767 and 442 is 13

Notice that 13 = HCF(26,13) = HCF(91,26) = HCF(117,91) = HCF(325,117) = HCF(442,325) = HCF(767,442) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 767, 442 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, 442?

Answer: HCF of 767, 442 is 13 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 767, 442 using Euclid's Algorithm?

Answer: For arbitrary numbers 767, 442 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.