Highest Common Factor of 608, 450, 672 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, 450, 672 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 608, 450, 672 is 2 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, 450, 672 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, 450, 672 is 2.

HCF(608, 450, 672) = 2

HCF of 608, 450, 672 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, 450, 672 is 2.

Highest Common Factor of 608,450,672 using Euclid's algorithm

Highest Common Factor of 608,450,672 is 2

Step 1: Since 608 > 450, we apply the division lemma to 608 and 450, to get

608 = 450 x 1 + 158

Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 158 and 450, to get

450 = 158 x 2 + 134

Step 3: We consider the new divisor 158 and the new remainder 134, and apply the division lemma to get

158 = 134 x 1 + 24

We consider the new divisor 134 and the new remainder 24,and apply the division lemma to get

134 = 24 x 5 + 14

We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get

24 = 14 x 1 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 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 608 and 450 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(134,24) = HCF(158,134) = HCF(450,158) = HCF(608,450) .

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

Step 1: Since 672 > 2, we apply the division lemma to 672 and 2, to get

672 = 2 x 336 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 672 is 2

Notice that 2 = HCF(672,2) .

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Frequently Asked Questions on HCF of 608, 450, 672 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, 450, 672?

Answer: HCF of 608, 450, 672 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 608, 450, 672 using Euclid's Algorithm?

Answer: For arbitrary numbers 608, 450, 672 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.