Highest Common Factor of 614, 976, 609 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 614, 976, 609 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 614, 976, 609 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 614, 976, 609 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 614, 976, 609 is 1.

HCF(614, 976, 609) = 1

HCF of 614, 976, 609 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 614, 976, 609 is 1.

Highest Common Factor of 614,976,609 using Euclid's algorithm

Highest Common Factor of 614,976,609 is 1

Step 1: Since 976 > 614, we apply the division lemma to 976 and 614, to get

976 = 614 x 1 + 362

Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 362 and 614, to get

614 = 362 x 1 + 252

Step 3: We consider the new divisor 362 and the new remainder 252, and apply the division lemma to get

362 = 252 x 1 + 110

We consider the new divisor 252 and the new remainder 110,and apply the division lemma to get

252 = 110 x 2 + 32

We consider the new divisor 110 and the new remainder 32,and apply the division lemma to get

110 = 32 x 3 + 14

We consider the new divisor 32 and the new remainder 14,and apply the division lemma to get

32 = 14 x 2 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 614 and 976 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(32,14) = HCF(110,32) = HCF(252,110) = HCF(362,252) = HCF(614,362) = HCF(976,614) .

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

Step 1: Since 609 > 2, we apply the division lemma to 609 and 2, to get

609 = 2 x 304 + 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 609 is 1

Notice that 1 = HCF(2,1) = HCF(609,2) .

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Frequently Asked Questions on HCF of 614, 976, 609 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 614, 976, 609?

Answer: HCF of 614, 976, 609 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 614, 976, 609 using Euclid's Algorithm?

Answer: For arbitrary numbers 614, 976, 609 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.