Highest Common Factor of 657, 8055, 7087 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 657, 8055, 7087 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 657, 8055, 7087 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 657, 8055, 7087 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 657, 8055, 7087 is 1.

HCF(657, 8055, 7087) = 1

HCF of 657, 8055, 7087 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 657, 8055, 7087 is 1.

Highest Common Factor of 657,8055,7087 using Euclid's algorithm

Highest Common Factor of 657,8055,7087 is 1

Step 1: Since 8055 > 657, we apply the division lemma to 8055 and 657, to get

8055 = 657 x 12 + 171

Step 2: Since the reminder 657 ≠ 0, we apply division lemma to 171 and 657, to get

657 = 171 x 3 + 144

Step 3: We consider the new divisor 171 and the new remainder 144, and apply the division lemma to get

171 = 144 x 1 + 27

We consider the new divisor 144 and the new remainder 27,and apply the division lemma to get

144 = 27 x 5 + 9

We consider the new divisor 27 and the new remainder 9,and apply the division lemma to get

27 = 9 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 657 and 8055 is 9

Notice that 9 = HCF(27,9) = HCF(144,27) = HCF(171,144) = HCF(657,171) = HCF(8055,657) .

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

Step 1: Since 7087 > 9, we apply the division lemma to 7087 and 9, to get

7087 = 9 x 787 + 4

Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 4 and 9, to get

9 = 4 x 2 + 1

Step 3: We consider the new divisor 4 and the new remainder 1, and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9 and 7087 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(7087,9) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 657, 8055, 7087 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 657, 8055, 7087?

Answer: HCF of 657, 8055, 7087 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 657, 8055, 7087 using Euclid's Algorithm?

Answer: For arbitrary numbers 657, 8055, 7087 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.