Highest Common Factor of 988, 1716, 6971 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 988, 1716, 6971 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 988, 1716, 6971 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 988, 1716, 6971 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 988, 1716, 6971 is 1.

HCF(988, 1716, 6971) = 1

HCF of 988, 1716, 6971 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 988, 1716, 6971 is 1.

Highest Common Factor of 988,1716,6971 using Euclid's algorithm

Highest Common Factor of 988,1716,6971 is 1

Step 1: Since 1716 > 988, we apply the division lemma to 1716 and 988, to get

1716 = 988 x 1 + 728

Step 2: Since the reminder 988 ≠ 0, we apply division lemma to 728 and 988, to get

988 = 728 x 1 + 260

Step 3: We consider the new divisor 728 and the new remainder 260, and apply the division lemma to get

728 = 260 x 2 + 208

We consider the new divisor 260 and the new remainder 208,and apply the division lemma to get

260 = 208 x 1 + 52

We consider the new divisor 208 and the new remainder 52,and apply the division lemma to get

208 = 52 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 52, the HCF of 988 and 1716 is 52

Notice that 52 = HCF(208,52) = HCF(260,208) = HCF(728,260) = HCF(988,728) = HCF(1716,988) .

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

Step 1: Since 6971 > 52, we apply the division lemma to 6971 and 52, to get

6971 = 52 x 134 + 3

Step 2: Since the reminder 52 ≠ 0, we apply division lemma to 3 and 52, to get

52 = 3 x 17 + 1

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

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 52 and 6971 is 1

Notice that 1 = HCF(3,1) = HCF(52,3) = HCF(6971,52) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 988, 1716, 6971 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 988, 1716, 6971?

Answer: HCF of 988, 1716, 6971 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 988, 1716, 6971 using Euclid's Algorithm?

Answer: For arbitrary numbers 988, 1716, 6971 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.