Highest Common Factor of 6524, 1843, 11666 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 6524, 1843, 11666 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6524, 1843, 11666 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 6524, 1843, 11666 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 6524, 1843, 11666 is 1.

HCF(6524, 1843, 11666) = 1

HCF of 6524, 1843, 11666 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 6524, 1843, 11666 is 1.

Highest Common Factor of 6524,1843,11666 using Euclid's algorithm

Highest Common Factor of 6524,1843,11666 is 1

Step 1: Since 6524 > 1843, we apply the division lemma to 6524 and 1843, to get

6524 = 1843 x 3 + 995

Step 2: Since the reminder 1843 ≠ 0, we apply division lemma to 995 and 1843, to get

1843 = 995 x 1 + 848

Step 3: We consider the new divisor 995 and the new remainder 848, and apply the division lemma to get

995 = 848 x 1 + 147

We consider the new divisor 848 and the new remainder 147,and apply the division lemma to get

848 = 147 x 5 + 113

We consider the new divisor 147 and the new remainder 113,and apply the division lemma to get

147 = 113 x 1 + 34

We consider the new divisor 113 and the new remainder 34,and apply the division lemma to get

113 = 34 x 3 + 11

We consider the new divisor 34 and the new remainder 11,and apply the division lemma to get

34 = 11 x 3 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6524 and 1843 is 1

Notice that 1 = HCF(11,1) = HCF(34,11) = HCF(113,34) = HCF(147,113) = HCF(848,147) = HCF(995,848) = HCF(1843,995) = HCF(6524,1843) .

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

Step 1: Since 11666 > 1, we apply the division lemma to 11666 and 1, to get

11666 = 1 x 11666 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 11666 is 1

Notice that 1 = HCF(11666,1) .

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Frequently Asked Questions on HCF of 6524, 1843, 11666 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 6524, 1843, 11666?

Answer: HCF of 6524, 1843, 11666 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6524, 1843, 11666 using Euclid's Algorithm?

Answer: For arbitrary numbers 6524, 1843, 11666 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.