Highest Common Factor of 7987, 916 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 7987, 916 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7987, 916 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 7987, 916 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 7987, 916 is 1.

HCF(7987, 916) = 1

HCF of 7987, 916 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 7987, 916 is 1.

Highest Common Factor of 7987,916 using Euclid's algorithm

Highest Common Factor of 7987,916 is 1

Step 1: Since 7987 > 916, we apply the division lemma to 7987 and 916, to get

7987 = 916 x 8 + 659

Step 2: Since the reminder 916 ≠ 0, we apply division lemma to 659 and 916, to get

916 = 659 x 1 + 257

Step 3: We consider the new divisor 659 and the new remainder 257, and apply the division lemma to get

659 = 257 x 2 + 145

We consider the new divisor 257 and the new remainder 145,and apply the division lemma to get

257 = 145 x 1 + 112

We consider the new divisor 145 and the new remainder 112,and apply the division lemma to get

145 = 112 x 1 + 33

We consider the new divisor 112 and the new remainder 33,and apply the division lemma to get

112 = 33 x 3 + 13

We consider the new divisor 33 and the new remainder 13,and apply the division lemma to get

33 = 13 x 2 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 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 7987 and 916 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(33,13) = HCF(112,33) = HCF(145,112) = HCF(257,145) = HCF(659,257) = HCF(916,659) = HCF(7987,916) .

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Frequently Asked Questions on HCF of 7987, 916 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 7987, 916?

Answer: HCF of 7987, 916 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7987, 916 using Euclid's Algorithm?

Answer: For arbitrary numbers 7987, 916 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.