Highest Common Factor of 612, 965, 351 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, 965, 351 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 612, 965, 351 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, 965, 351 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, 965, 351 is 1.

HCF(612, 965, 351) = 1

HCF of 612, 965, 351 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, 965, 351 is 1.

Highest Common Factor of 612,965,351 using Euclid's algorithm

Highest Common Factor of 612,965,351 is 1

Step 1: Since 965 > 612, we apply the division lemma to 965 and 612, to get

965 = 612 x 1 + 353

Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 353 and 612, to get

612 = 353 x 1 + 259

Step 3: We consider the new divisor 353 and the new remainder 259, and apply the division lemma to get

353 = 259 x 1 + 94

We consider the new divisor 259 and the new remainder 94,and apply the division lemma to get

259 = 94 x 2 + 71

We consider the new divisor 94 and the new remainder 71,and apply the division lemma to get

94 = 71 x 1 + 23

We consider the new divisor 71 and the new remainder 23,and apply the division lemma to get

71 = 23 x 3 + 2

We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get

23 = 2 x 11 + 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 612 and 965 is 1

Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(71,23) = HCF(94,71) = HCF(259,94) = HCF(353,259) = HCF(612,353) = HCF(965,612) .

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

Step 1: Since 351 > 1, we apply the division lemma to 351 and 1, to get

351 = 1 x 351 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 351 is 1

Notice that 1 = HCF(351,1) .

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Frequently Asked Questions on HCF of 612, 965, 351 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, 965, 351?

Answer: HCF of 612, 965, 351 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 612, 965, 351 using Euclid's Algorithm?

Answer: For arbitrary numbers 612, 965, 351 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.