Highest Common Factor of 974, 559, 344 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, 559, 344 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 974, 559, 344 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, 559, 344 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, 559, 344 is 1.

HCF(974, 559, 344) = 1

HCF of 974, 559, 344 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, 559, 344 is 1.

Highest Common Factor of 974,559,344 using Euclid's algorithm

Highest Common Factor of 974,559,344 is 1

Step 1: Since 974 > 559, we apply the division lemma to 974 and 559, to get

974 = 559 x 1 + 415

Step 2: Since the reminder 559 ≠ 0, we apply division lemma to 415 and 559, to get

559 = 415 x 1 + 144

Step 3: We consider the new divisor 415 and the new remainder 144, and apply the division lemma to get

415 = 144 x 2 + 127

We consider the new divisor 144 and the new remainder 127,and apply the division lemma to get

144 = 127 x 1 + 17

We consider the new divisor 127 and the new remainder 17,and apply the division lemma to get

127 = 17 x 7 + 8

We consider the new divisor 17 and the new remainder 8,and apply the division lemma to get

17 = 8 x 2 + 1

We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 974 and 559 is 1

Notice that 1 = HCF(8,1) = HCF(17,8) = HCF(127,17) = HCF(144,127) = HCF(415,144) = HCF(559,415) = HCF(974,559) .

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

Step 1: Since 344 > 1, we apply the division lemma to 344 and 1, to get

344 = 1 x 344 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 344 is 1

Notice that 1 = HCF(344,1) .

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Frequently Asked Questions on HCF of 974, 559, 344 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, 559, 344?

Answer: HCF of 974, 559, 344 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 974, 559, 344 using Euclid's Algorithm?

Answer: For arbitrary numbers 974, 559, 344 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.