Highest Common Factor of 502, 656, 763, 728 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 502, 656, 763, 728 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 502, 656, 763, 728 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 502, 656, 763, 728 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 502, 656, 763, 728 is 1.

HCF(502, 656, 763, 728) = 1

HCF of 502, 656, 763, 728 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 502, 656, 763, 728 is 1.

Highest Common Factor of 502,656,763,728 using Euclid's algorithm

Highest Common Factor of 502,656,763,728 is 1

Step 1: Since 656 > 502, we apply the division lemma to 656 and 502, to get

656 = 502 x 1 + 154

Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 154 and 502, to get

502 = 154 x 3 + 40

Step 3: We consider the new divisor 154 and the new remainder 40, and apply the division lemma to get

154 = 40 x 3 + 34

We consider the new divisor 40 and the new remainder 34,and apply the division lemma to get

40 = 34 x 1 + 6

We consider the new divisor 34 and the new remainder 6,and apply the division lemma to get

34 = 6 x 5 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 502 and 656 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(34,6) = HCF(40,34) = HCF(154,40) = HCF(502,154) = HCF(656,502) .

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

Step 1: Since 763 > 2, we apply the division lemma to 763 and 2, to get

763 = 2 x 381 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 763 is 1

Notice that 1 = HCF(2,1) = HCF(763,2) .

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

Step 1: Since 728 > 1, we apply the division lemma to 728 and 1, to get

728 = 1 x 728 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 728 is 1

Notice that 1 = HCF(728,1) .

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Frequently Asked Questions on HCF of 502, 656, 763, 728 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 502, 656, 763, 728?

Answer: HCF of 502, 656, 763, 728 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 502, 656, 763, 728 using Euclid's Algorithm?

Answer: For arbitrary numbers 502, 656, 763, 728 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.