Highest Common Factor of 8242, 9984, 64639 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 8242, 9984, 64639 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8242, 9984, 64639 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 8242, 9984, 64639 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 8242, 9984, 64639 is 1.

HCF(8242, 9984, 64639) = 1

HCF of 8242, 9984, 64639 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 8242, 9984, 64639 is 1.

Highest Common Factor of 8242,9984,64639 using Euclid's algorithm

Highest Common Factor of 8242,9984,64639 is 1

Step 1: Since 9984 > 8242, we apply the division lemma to 9984 and 8242, to get

9984 = 8242 x 1 + 1742

Step 2: Since the reminder 8242 ≠ 0, we apply division lemma to 1742 and 8242, to get

8242 = 1742 x 4 + 1274

Step 3: We consider the new divisor 1742 and the new remainder 1274, and apply the division lemma to get

1742 = 1274 x 1 + 468

We consider the new divisor 1274 and the new remainder 468,and apply the division lemma to get

1274 = 468 x 2 + 338

We consider the new divisor 468 and the new remainder 338,and apply the division lemma to get

468 = 338 x 1 + 130

We consider the new divisor 338 and the new remainder 130,and apply the division lemma to get

338 = 130 x 2 + 78

We consider the new divisor 130 and the new remainder 78,and apply the division lemma to get

130 = 78 x 1 + 52

We consider the new divisor 78 and the new remainder 52,and apply the division lemma to get

78 = 52 x 1 + 26

We consider the new divisor 52 and the new remainder 26,and apply the division lemma to get

52 = 26 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 26, the HCF of 8242 and 9984 is 26

Notice that 26 = HCF(52,26) = HCF(78,52) = HCF(130,78) = HCF(338,130) = HCF(468,338) = HCF(1274,468) = HCF(1742,1274) = HCF(8242,1742) = HCF(9984,8242) .

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

Step 1: Since 64639 > 26, we apply the division lemma to 64639 and 26, to get

64639 = 26 x 2486 + 3

Step 2: Since the reminder 26 ≠ 0, we apply division lemma to 3 and 26, to get

26 = 3 x 8 + 2

Step 3: 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 26 and 64639 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(26,3) = HCF(64639,26) .

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Frequently Asked Questions on HCF of 8242, 9984, 64639 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 8242, 9984, 64639?

Answer: HCF of 8242, 9984, 64639 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8242, 9984, 64639 using Euclid's Algorithm?

Answer: For arbitrary numbers 8242, 9984, 64639 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.