Highest Common Factor of 237, 782 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 237, 782 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 237, 782 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 237, 782 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 237, 782 is 1.

HCF(237, 782) = 1

HCF of 237, 782 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 237, 782 is 1.

Highest Common Factor of 237,782 using Euclid's algorithm

Highest Common Factor of 237,782 is 1

Step 1: Since 782 > 237, we apply the division lemma to 782 and 237, to get

782 = 237 x 3 + 71

Step 2: Since the reminder 237 ≠ 0, we apply division lemma to 71 and 237, to get

237 = 71 x 3 + 24

Step 3: We consider the new divisor 71 and the new remainder 24, and apply the division lemma to get

71 = 24 x 2 + 23

We consider the new divisor 24 and the new remainder 23,and apply the division lemma to get

24 = 23 x 1 + 1

We consider the new divisor 23 and the new remainder 1,and apply the division lemma to get

23 = 1 x 23 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 237 and 782 is 1

Notice that 1 = HCF(23,1) = HCF(24,23) = HCF(71,24) = HCF(237,71) = HCF(782,237) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 237, 782 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 237, 782?

Answer: HCF of 237, 782 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 237, 782 using Euclid's Algorithm?

Answer: For arbitrary numbers 237, 782 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.