Highest Common Factor of 920, 672, 475 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 920, 672, 475 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 920, 672, 475 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 920, 672, 475 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 920, 672, 475 is 1.

HCF(920, 672, 475) = 1

HCF of 920, 672, 475 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 920, 672, 475 is 1.

Highest Common Factor of 920,672,475 using Euclid's algorithm

Highest Common Factor of 920,672,475 is 1

Step 1: Since 920 > 672, we apply the division lemma to 920 and 672, to get

920 = 672 x 1 + 248

Step 2: Since the reminder 672 ≠ 0, we apply division lemma to 248 and 672, to get

672 = 248 x 2 + 176

Step 3: We consider the new divisor 248 and the new remainder 176, and apply the division lemma to get

248 = 176 x 1 + 72

We consider the new divisor 176 and the new remainder 72,and apply the division lemma to get

176 = 72 x 2 + 32

We consider the new divisor 72 and the new remainder 32,and apply the division lemma to get

72 = 32 x 2 + 8

We consider the new divisor 32 and the new remainder 8,and apply the division lemma to get

32 = 8 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 920 and 672 is 8

Notice that 8 = HCF(32,8) = HCF(72,32) = HCF(176,72) = HCF(248,176) = HCF(672,248) = HCF(920,672) .

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

Step 1: Since 475 > 8, we apply the division lemma to 475 and 8, to get

475 = 8 x 59 + 3

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 3 and 8, to get

8 = 3 x 2 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 8 and 475 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(475,8) .

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Frequently Asked Questions on HCF of 920, 672, 475 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 920, 672, 475?

Answer: HCF of 920, 672, 475 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 920, 672, 475 using Euclid's Algorithm?

Answer: For arbitrary numbers 920, 672, 475 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.