Highest Common Factor of 756, 360 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 756, 360 i.e. 36 the largest integer that leaves a remainder zero for all numbers.

HCF of 756, 360 is 36 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 756, 360 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 756, 360 is 36.

HCF(756, 360) = 36

HCF of 756, 360 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 756, 360 is 36.

Highest Common Factor of 756,360 using Euclid's algorithm

Highest Common Factor of 756,360 is 36

Step 1: Since 756 > 360, we apply the division lemma to 756 and 360, to get

756 = 360 x 2 + 36

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 36 and 360, to get

360 = 36 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 756 and 360 is 36

Notice that 36 = HCF(360,36) = HCF(756,360) .

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Frequently Asked Questions on HCF of 756, 360 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 756, 360?

Answer: HCF of 756, 360 is 36 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 756, 360 using Euclid's Algorithm?

Answer: For arbitrary numbers 756, 360 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.