Highest Common Factor of 574, 971, 256 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 574, 971, 256 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 574, 971, 256 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 574, 971, 256 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 574, 971, 256 is 1.

HCF(574, 971, 256) = 1

HCF of 574, 971, 256 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 574, 971, 256 is 1.

Highest Common Factor of 574,971,256 using Euclid's algorithm

Highest Common Factor of 574,971,256 is 1

Step 1: Since 971 > 574, we apply the division lemma to 971 and 574, to get

971 = 574 x 1 + 397

Step 2: Since the reminder 574 ≠ 0, we apply division lemma to 397 and 574, to get

574 = 397 x 1 + 177

Step 3: We consider the new divisor 397 and the new remainder 177, and apply the division lemma to get

397 = 177 x 2 + 43

We consider the new divisor 177 and the new remainder 43,and apply the division lemma to get

177 = 43 x 4 + 5

We consider the new divisor 43 and the new remainder 5,and apply the division lemma to get

43 = 5 x 8 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 574 and 971 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(43,5) = HCF(177,43) = HCF(397,177) = HCF(574,397) = HCF(971,574) .

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

Step 1: Since 256 > 1, we apply the division lemma to 256 and 1, to get

256 = 1 x 256 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 256 is 1

Notice that 1 = HCF(256,1) .

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Frequently Asked Questions on HCF of 574, 971, 256 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 574, 971, 256?

Answer: HCF of 574, 971, 256 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 574, 971, 256 using Euclid's Algorithm?

Answer: For arbitrary numbers 574, 971, 256 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.