# Highest Common Factor of 422, 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 422, 692 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 422, 692 is 2 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 422, 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 422, 692 is 2.

HCF(422, 692) = 2

## HCF of 422, 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 422, 692 is 2. ### Highest Common Factor of 422,692 is 2

Step 1: Since 692 > 422, we apply the division lemma to 692 and 422, to get

692 = 422 x 1 + 270

Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 270 and 422, to get

422 = 270 x 1 + 152

Step 3: We consider the new divisor 270 and the new remainder 152, and apply the division lemma to get

270 = 152 x 1 + 118

We consider the new divisor 152 and the new remainder 118,and apply the division lemma to get

152 = 118 x 1 + 34

We consider the new divisor 118 and the new remainder 34,and apply the division lemma to get

118 = 34 x 3 + 16

We consider the new divisor 34 and the new remainder 16,and apply the division lemma to get

34 = 16 x 2 + 2

We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get

16 = 2 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 422 and 692 is 2

Notice that 2 = HCF(16,2) = HCF(34,16) = HCF(118,34) = HCF(152,118) = HCF(270,152) = HCF(422,270) = HCF(692,422) .

### HCF using Euclid's Algorithm Calculation Examples

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

### Frequently Asked Questions on HCF of 422, 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 422, 692?

Answer: HCF of 422, 692 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 422, 692 using Euclid's Algorithm?

Answer: For arbitrary numbers 422, 692 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.