Highest Common Factor of 612, 446, 431 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 612, 446, 431 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 612, 446, 431 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 612, 446, 431 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 612, 446, 431 is 1.

HCF(612, 446, 431) = 1

HCF of 612, 446, 431 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 612, 446, 431 is 1.

Highest Common Factor of 612,446,431 using Euclid's algorithm

Highest Common Factor of 612,446,431 is 1

Step 1: Since 612 > 446, we apply the division lemma to 612 and 446, to get

612 = 446 x 1 + 166

Step 2: Since the reminder 446 ≠ 0, we apply division lemma to 166 and 446, to get

446 = 166 x 2 + 114

Step 3: We consider the new divisor 166 and the new remainder 114, and apply the division lemma to get

166 = 114 x 1 + 52

We consider the new divisor 114 and the new remainder 52,and apply the division lemma to get

114 = 52 x 2 + 10

We consider the new divisor 52 and the new remainder 10,and apply the division lemma to get

52 = 10 x 5 + 2

We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get

10 = 2 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 612 and 446 is 2

Notice that 2 = HCF(10,2) = HCF(52,10) = HCF(114,52) = HCF(166,114) = HCF(446,166) = HCF(612,446) .

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

Step 1: Since 431 > 2, we apply the division lemma to 431 and 2, to get

431 = 2 x 215 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 431 is 1

Notice that 1 = HCF(2,1) = HCF(431,2) .

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Frequently Asked Questions on HCF of 612, 446, 431 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 612, 446, 431?

Answer: HCF of 612, 446, 431 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 612, 446, 431 using Euclid's Algorithm?

Answer: For arbitrary numbers 612, 446, 431 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.