Highest Common Factor of 765, 472, 220 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 765, 472, 220 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 765, 472, 220 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 765, 472, 220 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 765, 472, 220 is 1.

HCF(765, 472, 220) = 1

HCF of 765, 472, 220 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 765, 472, 220 is 1.

Highest Common Factor of 765,472,220 using Euclid's algorithm

Highest Common Factor of 765,472,220 is 1

Step 1: Since 765 > 472, we apply the division lemma to 765 and 472, to get

765 = 472 x 1 + 293

Step 2: Since the reminder 472 ≠ 0, we apply division lemma to 293 and 472, to get

472 = 293 x 1 + 179

Step 3: We consider the new divisor 293 and the new remainder 179, and apply the division lemma to get

293 = 179 x 1 + 114

We consider the new divisor 179 and the new remainder 114,and apply the division lemma to get

179 = 114 x 1 + 65

We consider the new divisor 114 and the new remainder 65,and apply the division lemma to get

114 = 65 x 1 + 49

We consider the new divisor 65 and the new remainder 49,and apply the division lemma to get

65 = 49 x 1 + 16

We consider the new divisor 49 and the new remainder 16,and apply the division lemma to get

49 = 16 x 3 + 1

We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get

16 = 1 x 16 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 765 and 472 is 1

Notice that 1 = HCF(16,1) = HCF(49,16) = HCF(65,49) = HCF(114,65) = HCF(179,114) = HCF(293,179) = HCF(472,293) = HCF(765,472) .

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

Step 1: Since 220 > 1, we apply the division lemma to 220 and 1, to get

220 = 1 x 220 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 220 is 1

Notice that 1 = HCF(220,1) .

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Frequently Asked Questions on HCF of 765, 472, 220 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 765, 472, 220?

Answer: HCF of 765, 472, 220 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 765, 472, 220 using Euclid's Algorithm?

Answer: For arbitrary numbers 765, 472, 220 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.