Highest Common Factor of 312, 812, 875 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 312, 812, 875 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 312, 812, 875 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 312, 812, 875 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 312, 812, 875 is 1.

HCF(312, 812, 875) = 1

HCF of 312, 812, 875 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 312, 812, 875 is 1.

Highest Common Factor of 312,812,875 using Euclid's algorithm

Highest Common Factor of 312,812,875 is 1

Step 1: Since 812 > 312, we apply the division lemma to 812 and 312, to get

812 = 312 x 2 + 188

Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 188 and 312, to get

312 = 188 x 1 + 124

Step 3: We consider the new divisor 188 and the new remainder 124, and apply the division lemma to get

188 = 124 x 1 + 64

We consider the new divisor 124 and the new remainder 64,and apply the division lemma to get

124 = 64 x 1 + 60

We consider the new divisor 64 and the new remainder 60,and apply the division lemma to get

64 = 60 x 1 + 4

We consider the new divisor 60 and the new remainder 4,and apply the division lemma to get

60 = 4 x 15 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 312 and 812 is 4

Notice that 4 = HCF(60,4) = HCF(64,60) = HCF(124,64) = HCF(188,124) = HCF(312,188) = HCF(812,312) .

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

Step 1: Since 875 > 4, we apply the division lemma to 875 and 4, to get

875 = 4 x 218 + 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 875 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(875,4) .

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Frequently Asked Questions on HCF of 312, 812, 875 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 312, 812, 875?

Answer: HCF of 312, 812, 875 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 312, 812, 875 using Euclid's Algorithm?

Answer: For arbitrary numbers 312, 812, 875 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.