Highest Common Factor of 974, 606, 419 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 974, 606, 419 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 974, 606, 419 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 974, 606, 419 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 974, 606, 419 is 1.

HCF(974, 606, 419) = 1

HCF of 974, 606, 419 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 974, 606, 419 is 1.

Highest Common Factor of 974,606,419 using Euclid's algorithm

Highest Common Factor of 974,606,419 is 1

Step 1: Since 974 > 606, we apply the division lemma to 974 and 606, to get

974 = 606 x 1 + 368

Step 2: Since the reminder 606 ≠ 0, we apply division lemma to 368 and 606, to get

606 = 368 x 1 + 238

Step 3: We consider the new divisor 368 and the new remainder 238, and apply the division lemma to get

368 = 238 x 1 + 130

We consider the new divisor 238 and the new remainder 130,and apply the division lemma to get

238 = 130 x 1 + 108

We consider the new divisor 130 and the new remainder 108,and apply the division lemma to get

130 = 108 x 1 + 22

We consider the new divisor 108 and the new remainder 22,and apply the division lemma to get

108 = 22 x 4 + 20

We consider the new divisor 22 and the new remainder 20,and apply the division lemma to get

22 = 20 x 1 + 2

We consider the new divisor 20 and the new remainder 2,and apply the division lemma to get

20 = 2 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 974 and 606 is 2

Notice that 2 = HCF(20,2) = HCF(22,20) = HCF(108,22) = HCF(130,108) = HCF(238,130) = HCF(368,238) = HCF(606,368) = HCF(974,606) .

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

Step 1: Since 419 > 2, we apply the division lemma to 419 and 2, to get

419 = 2 x 209 + 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 419 is 1

Notice that 1 = HCF(2,1) = HCF(419,2) .

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Frequently Asked Questions on HCF of 974, 606, 419 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 974, 606, 419?

Answer: HCF of 974, 606, 419 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 974, 606, 419 using Euclid's Algorithm?

Answer: For arbitrary numbers 974, 606, 419 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.