Highest Common Factor of 9910, 2746, 64563 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 9910, 2746, 64563 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 9910, 2746, 64563 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 9910, 2746, 64563 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 9910, 2746, 64563 is 1.

HCF(9910, 2746, 64563) = 1

HCF of 9910, 2746, 64563 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 9910, 2746, 64563 is 1.

Highest Common Factor of 9910,2746,64563 using Euclid's algorithm

Highest Common Factor of 9910,2746,64563 is 1

Step 1: Since 9910 > 2746, we apply the division lemma to 9910 and 2746, to get

9910 = 2746 x 3 + 1672

Step 2: Since the reminder 2746 ≠ 0, we apply division lemma to 1672 and 2746, to get

2746 = 1672 x 1 + 1074

Step 3: We consider the new divisor 1672 and the new remainder 1074, and apply the division lemma to get

1672 = 1074 x 1 + 598

We consider the new divisor 1074 and the new remainder 598,and apply the division lemma to get

1074 = 598 x 1 + 476

We consider the new divisor 598 and the new remainder 476,and apply the division lemma to get

598 = 476 x 1 + 122

We consider the new divisor 476 and the new remainder 122,and apply the division lemma to get

476 = 122 x 3 + 110

We consider the new divisor 122 and the new remainder 110,and apply the division lemma to get

122 = 110 x 1 + 12

We consider the new divisor 110 and the new remainder 12,and apply the division lemma to get

110 = 12 x 9 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 9910 and 2746 is 2

Notice that 2 = HCF(12,2) = HCF(110,12) = HCF(122,110) = HCF(476,122) = HCF(598,476) = HCF(1074,598) = HCF(1672,1074) = HCF(2746,1672) = HCF(9910,2746) .

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

Step 1: Since 64563 > 2, we apply the division lemma to 64563 and 2, to get

64563 = 2 x 32281 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 64563 is 1

Notice that 1 = HCF(2,1) = HCF(64563,2) .

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Frequently Asked Questions on HCF of 9910, 2746, 64563 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 9910, 2746, 64563?

Answer: HCF of 9910, 2746, 64563 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 9910, 2746, 64563 using Euclid's Algorithm?

Answer: For arbitrary numbers 9910, 2746, 64563 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.