Highest Common Factor of 991, 718, 707 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 991, 718, 707 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 991, 718, 707 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 991, 718, 707 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 991, 718, 707 is 1.

HCF(991, 718, 707) = 1

HCF of 991, 718, 707 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 991, 718, 707 is 1.

Highest Common Factor of 991,718,707 using Euclid's algorithm

Highest Common Factor of 991,718,707 is 1

Step 1: Since 991 > 718, we apply the division lemma to 991 and 718, to get

991 = 718 x 1 + 273

Step 2: Since the reminder 718 ≠ 0, we apply division lemma to 273 and 718, to get

718 = 273 x 2 + 172

Step 3: We consider the new divisor 273 and the new remainder 172, and apply the division lemma to get

273 = 172 x 1 + 101

We consider the new divisor 172 and the new remainder 101,and apply the division lemma to get

172 = 101 x 1 + 71

We consider the new divisor 101 and the new remainder 71,and apply the division lemma to get

101 = 71 x 1 + 30

We consider the new divisor 71 and the new remainder 30,and apply the division lemma to get

71 = 30 x 2 + 11

We consider the new divisor 30 and the new remainder 11,and apply the division lemma to get

30 = 11 x 2 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 991 and 718 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(30,11) = HCF(71,30) = HCF(101,71) = HCF(172,101) = HCF(273,172) = HCF(718,273) = HCF(991,718) .

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

Step 1: Since 707 > 1, we apply the division lemma to 707 and 1, to get

707 = 1 x 707 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 707 is 1

Notice that 1 = HCF(707,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 991, 718, 707 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 991, 718, 707?

Answer: HCF of 991, 718, 707 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 991, 718, 707 using Euclid's Algorithm?

Answer: For arbitrary numbers 991, 718, 707 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.