Highest Common Factor of 574, 768, 977 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, 768, 977 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 574, 768, 977 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, 768, 977 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, 768, 977 is 1.

HCF(574, 768, 977) = 1

HCF of 574, 768, 977 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, 768, 977 is 1.

Highest Common Factor of 574,768,977 using Euclid's algorithm

Highest Common Factor of 574,768,977 is 1

Step 1: Since 768 > 574, we apply the division lemma to 768 and 574, to get

768 = 574 x 1 + 194

Step 2: Since the reminder 574 ≠ 0, we apply division lemma to 194 and 574, to get

574 = 194 x 2 + 186

Step 3: We consider the new divisor 194 and the new remainder 186, and apply the division lemma to get

194 = 186 x 1 + 8

We consider the new divisor 186 and the new remainder 8,and apply the division lemma to get

186 = 8 x 23 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 574 and 768 is 2

Notice that 2 = HCF(8,2) = HCF(186,8) = HCF(194,186) = HCF(574,194) = HCF(768,574) .

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

Step 1: Since 977 > 2, we apply the division lemma to 977 and 2, to get

977 = 2 x 488 + 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 977 is 1

Notice that 1 = HCF(2,1) = HCF(977,2) .

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Frequently Asked Questions on HCF of 574, 768, 977 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, 768, 977?

Answer: HCF of 574, 768, 977 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 574, 768, 977 using Euclid's Algorithm?

Answer: For arbitrary numbers 574, 768, 977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.