Highest Common Factor of 672, 255, 867 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 672, 255, 867 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 672, 255, 867 is 3 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 672, 255, 867 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 672, 255, 867 is 3.

HCF(672, 255, 867) = 3

HCF of 672, 255, 867 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 672, 255, 867 is 3.

Highest Common Factor of 672,255,867 using Euclid's algorithm

Highest Common Factor of 672,255,867 is 3

Step 1: Since 672 > 255, we apply the division lemma to 672 and 255, to get

672 = 255 x 2 + 162

Step 2: Since the reminder 255 ≠ 0, we apply division lemma to 162 and 255, to get

255 = 162 x 1 + 93

Step 3: We consider the new divisor 162 and the new remainder 93, and apply the division lemma to get

162 = 93 x 1 + 69

We consider the new divisor 93 and the new remainder 69,and apply the division lemma to get

93 = 69 x 1 + 24

We consider the new divisor 69 and the new remainder 24,and apply the division lemma to get

69 = 24 x 2 + 21

We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get

24 = 21 x 1 + 3

We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get

21 = 3 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 672 and 255 is 3

Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(69,24) = HCF(93,69) = HCF(162,93) = HCF(255,162) = HCF(672,255) .

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

Step 1: Since 867 > 3, we apply the division lemma to 867 and 3, to get

867 = 3 x 289 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 867 is 3

Notice that 3 = HCF(867,3) .

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Frequently Asked Questions on HCF of 672, 255, 867 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 672, 255, 867?

Answer: HCF of 672, 255, 867 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 672, 255, 867 using Euclid's Algorithm?

Answer: For arbitrary numbers 672, 255, 867 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.