Highest Common Factor of 2616, 9026, 43635 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 2616, 9026, 43635 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2616, 9026, 43635 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 2616, 9026, 43635 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 2616, 9026, 43635 is 1.

HCF(2616, 9026, 43635) = 1

HCF of 2616, 9026, 43635 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 2616, 9026, 43635 is 1.

Highest Common Factor of 2616,9026,43635 using Euclid's algorithm

Highest Common Factor of 2616,9026,43635 is 1

Step 1: Since 9026 > 2616, we apply the division lemma to 9026 and 2616, to get

9026 = 2616 x 3 + 1178

Step 2: Since the reminder 2616 ≠ 0, we apply division lemma to 1178 and 2616, to get

2616 = 1178 x 2 + 260

Step 3: We consider the new divisor 1178 and the new remainder 260, and apply the division lemma to get

1178 = 260 x 4 + 138

We consider the new divisor 260 and the new remainder 138,and apply the division lemma to get

260 = 138 x 1 + 122

We consider the new divisor 138 and the new remainder 122,and apply the division lemma to get

138 = 122 x 1 + 16

We consider the new divisor 122 and the new remainder 16,and apply the division lemma to get

122 = 16 x 7 + 10

We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get

16 = 10 x 1 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2616 and 9026 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(122,16) = HCF(138,122) = HCF(260,138) = HCF(1178,260) = HCF(2616,1178) = HCF(9026,2616) .

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

Step 1: Since 43635 > 2, we apply the division lemma to 43635 and 2, to get

43635 = 2 x 21817 + 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 43635 is 1

Notice that 1 = HCF(2,1) = HCF(43635,2) .

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Frequently Asked Questions on HCF of 2616, 9026, 43635 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 2616, 9026, 43635?

Answer: HCF of 2616, 9026, 43635 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2616, 9026, 43635 using Euclid's Algorithm?

Answer: For arbitrary numbers 2616, 9026, 43635 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.