Highest Common Factor of 608, 420, 27 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 608, 420, 27 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 608, 420, 27 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 608, 420, 27 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 608, 420, 27 is 1.

HCF(608, 420, 27) = 1

HCF of 608, 420, 27 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 608, 420, 27 is 1.

Highest Common Factor of 608,420,27 using Euclid's algorithm

Highest Common Factor of 608,420,27 is 1

Step 1: Since 608 > 420, we apply the division lemma to 608 and 420, to get

608 = 420 x 1 + 188

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 188 and 420, to get

420 = 188 x 2 + 44

Step 3: We consider the new divisor 188 and the new remainder 44, and apply the division lemma to get

188 = 44 x 4 + 12

We consider the new divisor 44 and the new remainder 12,and apply the division lemma to get

44 = 12 x 3 + 8

We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get

12 = 8 x 1 + 4

We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get

8 = 4 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 608 and 420 is 4

Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(44,12) = HCF(188,44) = HCF(420,188) = HCF(608,420) .

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

Step 1: Since 27 > 4, we apply the division lemma to 27 and 4, to get

27 = 4 x 6 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 27 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(27,4) .

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Frequently Asked Questions on HCF of 608, 420, 27 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 608, 420, 27?

Answer: HCF of 608, 420, 27 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 608, 420, 27 using Euclid's Algorithm?

Answer: For arbitrary numbers 608, 420, 27 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.