Highest Common Factor of 7987, 9827, 34774 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, 9827, 34774 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7987, 9827, 34774 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, 9827, 34774 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, 9827, 34774 is 1.

HCF(7987, 9827, 34774) = 1

HCF of 7987, 9827, 34774 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, 9827, 34774 is 1.

Highest Common Factor of 7987,9827,34774 using Euclid's algorithm

Highest Common Factor of 7987,9827,34774 is 1

Step 1: Since 9827 > 7987, we apply the division lemma to 9827 and 7987, to get

9827 = 7987 x 1 + 1840

Step 2: Since the reminder 7987 ≠ 0, we apply division lemma to 1840 and 7987, to get

7987 = 1840 x 4 + 627

Step 3: We consider the new divisor 1840 and the new remainder 627, and apply the division lemma to get

1840 = 627 x 2 + 586

We consider the new divisor 627 and the new remainder 586,and apply the division lemma to get

627 = 586 x 1 + 41

We consider the new divisor 586 and the new remainder 41,and apply the division lemma to get

586 = 41 x 14 + 12

We consider the new divisor 41 and the new remainder 12,and apply the division lemma to get

41 = 12 x 3 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 7987 and 9827 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(41,12) = HCF(586,41) = HCF(627,586) = HCF(1840,627) = HCF(7987,1840) = HCF(9827,7987) .

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

Step 1: Since 34774 > 1, we apply the division lemma to 34774 and 1, to get

34774 = 1 x 34774 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 34774 is 1

Notice that 1 = HCF(34774,1) .

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Frequently Asked Questions on HCF of 7987, 9827, 34774 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, 9827, 34774?

Answer: HCF of 7987, 9827, 34774 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7987, 9827, 34774 using Euclid's Algorithm?

Answer: For arbitrary numbers 7987, 9827, 34774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.