Highest Common Factor of 7678, 7961, 66319 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 7678, 7961, 66319 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7678, 7961, 66319 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 7678, 7961, 66319 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 7678, 7961, 66319 is 1.

HCF(7678, 7961, 66319) = 1

HCF of 7678, 7961, 66319 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 7678, 7961, 66319 is 1.

Highest Common Factor of 7678,7961,66319 using Euclid's algorithm

Highest Common Factor of 7678,7961,66319 is 1

Step 1: Since 7961 > 7678, we apply the division lemma to 7961 and 7678, to get

7961 = 7678 x 1 + 283

Step 2: Since the reminder 7678 ≠ 0, we apply division lemma to 283 and 7678, to get

7678 = 283 x 27 + 37

Step 3: We consider the new divisor 283 and the new remainder 37, and apply the division lemma to get

283 = 37 x 7 + 24

We consider the new divisor 37 and the new remainder 24,and apply the division lemma to get

37 = 24 x 1 + 13

We consider the new divisor 24 and the new remainder 13,and apply the division lemma to get

24 = 13 x 1 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 7678 and 7961 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(37,24) = HCF(283,37) = HCF(7678,283) = HCF(7961,7678) .

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

Step 1: Since 66319 > 1, we apply the division lemma to 66319 and 1, to get

66319 = 1 x 66319 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 66319 is 1

Notice that 1 = HCF(66319,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 7678, 7961, 66319 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 7678, 7961, 66319?

Answer: HCF of 7678, 7961, 66319 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7678, 7961, 66319 using Euclid's Algorithm?

Answer: For arbitrary numbers 7678, 7961, 66319 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.