Highest Common Factor of 714, 497, 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 714, 497, 220 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 714, 497, 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 714, 497, 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 714, 497, 220 is 1.

HCF(714, 497, 220) = 1

HCF of 714, 497, 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 714, 497, 220 is 1.

Highest Common Factor of 714,497,220 using Euclid's algorithm

Highest Common Factor of 714,497,220 is 1

Step 1: Since 714 > 497, we apply the division lemma to 714 and 497, to get

714 = 497 x 1 + 217

Step 2: Since the reminder 497 ≠ 0, we apply division lemma to 217 and 497, to get

497 = 217 x 2 + 63

Step 3: We consider the new divisor 217 and the new remainder 63, and apply the division lemma to get

217 = 63 x 3 + 28

We consider the new divisor 63 and the new remainder 28,and apply the division lemma to get

63 = 28 x 2 + 7

We consider the new divisor 28 and the new remainder 7,and apply the division lemma to get

28 = 7 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 714 and 497 is 7

Notice that 7 = HCF(28,7) = HCF(63,28) = HCF(217,63) = HCF(497,217) = HCF(714,497) .

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

Step 1: Since 220 > 7, we apply the division lemma to 220 and 7, to get

220 = 7 x 31 + 3

Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 3 and 7, to get

7 = 3 x 2 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 220 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(220,7) .

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Frequently Asked Questions on HCF of 714, 497, 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 714, 497, 220?

Answer: HCF of 714, 497, 220 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 714, 497, 220 using Euclid's Algorithm?

Answer: For arbitrary numbers 714, 497, 220 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.