Highest Common Factor of 778, 577 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 778, 577 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 778, 577 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 778, 577 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 778, 577 is 1.

HCF(778, 577) = 1

HCF of 778, 577 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 778, 577 is 1.

Highest Common Factor of 778,577 using Euclid's algorithm

Highest Common Factor of 778,577 is 1

Step 1: Since 778 > 577, we apply the division lemma to 778 and 577, to get

778 = 577 x 1 + 201

Step 2: Since the reminder 577 ≠ 0, we apply division lemma to 201 and 577, to get

577 = 201 x 2 + 175

Step 3: We consider the new divisor 201 and the new remainder 175, and apply the division lemma to get

201 = 175 x 1 + 26

We consider the new divisor 175 and the new remainder 26,and apply the division lemma to get

175 = 26 x 6 + 19

We consider the new divisor 26 and the new remainder 19,and apply the division lemma to get

26 = 19 x 1 + 7

We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get

19 = 7 x 2 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 778 and 577 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(26,19) = HCF(175,26) = HCF(201,175) = HCF(577,201) = HCF(778,577) .

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Frequently Asked Questions on HCF of 778, 577 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 778, 577?

Answer: HCF of 778, 577 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 778, 577 using Euclid's Algorithm?

Answer: For arbitrary numbers 778, 577 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.