Highest Common Factor of 716, 929, 31 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 716, 929, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 716, 929, 31 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 716, 929, 31 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 716, 929, 31 is 1.

HCF(716, 929, 31) = 1

HCF of 716, 929, 31 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 716, 929, 31 is 1.

Highest Common Factor of 716,929,31 using Euclid's algorithm

Highest Common Factor of 716,929,31 is 1

Step 1: Since 929 > 716, we apply the division lemma to 929 and 716, to get

929 = 716 x 1 + 213

Step 2: Since the reminder 716 ≠ 0, we apply division lemma to 213 and 716, to get

716 = 213 x 3 + 77

Step 3: We consider the new divisor 213 and the new remainder 77, and apply the division lemma to get

213 = 77 x 2 + 59

We consider the new divisor 77 and the new remainder 59,and apply the division lemma to get

77 = 59 x 1 + 18

We consider the new divisor 59 and the new remainder 18,and apply the division lemma to get

59 = 18 x 3 + 5

We consider the new divisor 18 and the new remainder 5,and apply the division lemma to get

18 = 5 x 3 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 716 and 929 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(18,5) = HCF(59,18) = HCF(77,59) = HCF(213,77) = HCF(716,213) = HCF(929,716) .

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

Step 1: Since 31 > 1, we apply the division lemma to 31 and 1, to get

31 = 1 x 31 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31 is 1

Notice that 1 = HCF(31,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 716, 929, 31 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 716, 929, 31?

Answer: HCF of 716, 929, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 716, 929, 31 using Euclid's Algorithm?

Answer: For arbitrary numbers 716, 929, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.