Highest Common Factor of 757, 7987 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 757, 7987 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 757, 7987 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 757, 7987 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 757, 7987 is 1.

HCF(757, 7987) = 1

HCF of 757, 7987 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 757, 7987 is 1.

Highest Common Factor of 757,7987 using Euclid's algorithm

Highest Common Factor of 757,7987 is 1

Step 1: Since 7987 > 757, we apply the division lemma to 7987 and 757, to get

7987 = 757 x 10 + 417

Step 2: Since the reminder 757 ≠ 0, we apply division lemma to 417 and 757, to get

757 = 417 x 1 + 340

Step 3: We consider the new divisor 417 and the new remainder 340, and apply the division lemma to get

417 = 340 x 1 + 77

We consider the new divisor 340 and the new remainder 77,and apply the division lemma to get

340 = 77 x 4 + 32

We consider the new divisor 77 and the new remainder 32,and apply the division lemma to get

77 = 32 x 2 + 13

We consider the new divisor 32 and the new remainder 13,and apply the division lemma to get

32 = 13 x 2 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 757 and 7987 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(32,13) = HCF(77,32) = HCF(340,77) = HCF(417,340) = HCF(757,417) = HCF(7987,757) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 757, 7987 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 757, 7987?

Answer: HCF of 757, 7987 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 757, 7987 using Euclid's Algorithm?

Answer: For arbitrary numbers 757, 7987 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.