Highest Common Factor of 523, 7678, 3606 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 523, 7678, 3606 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 523, 7678, 3606 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 523, 7678, 3606 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 523, 7678, 3606 is 1.

HCF(523, 7678, 3606) = 1

HCF of 523, 7678, 3606 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 523, 7678, 3606 is 1.

Highest Common Factor of 523,7678,3606 using Euclid's algorithm

Highest Common Factor of 523,7678,3606 is 1

Step 1: Since 7678 > 523, we apply the division lemma to 7678 and 523, to get

7678 = 523 x 14 + 356

Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 356 and 523, to get

523 = 356 x 1 + 167

Step 3: We consider the new divisor 356 and the new remainder 167, and apply the division lemma to get

356 = 167 x 2 + 22

We consider the new divisor 167 and the new remainder 22,and apply the division lemma to get

167 = 22 x 7 + 13

We consider the new divisor 22 and the new remainder 13,and apply the division lemma to get

22 = 13 x 1 + 9

We consider the new divisor 13 and the new remainder 9,and apply the division lemma to get

13 = 9 x 1 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 523 and 7678 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(13,9) = HCF(22,13) = HCF(167,22) = HCF(356,167) = HCF(523,356) = HCF(7678,523) .

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

Step 1: Since 3606 > 1, we apply the division lemma to 3606 and 1, to get

3606 = 1 x 3606 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3606 is 1

Notice that 1 = HCF(3606,1) .

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Frequently Asked Questions on HCF of 523, 7678, 3606 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 523, 7678, 3606?

Answer: HCF of 523, 7678, 3606 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 523, 7678, 3606 using Euclid's Algorithm?

Answer: For arbitrary numbers 523, 7678, 3606 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.