Highest Common Factor of 490, 777, 767 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 490, 777, 767 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 490, 777, 767 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 490, 777, 767 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 490, 777, 767 is 1.

HCF(490, 777, 767) = 1

HCF of 490, 777, 767 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 490, 777, 767 is 1.

Highest Common Factor of 490,777,767 using Euclid's algorithm

Highest Common Factor of 490,777,767 is 1

Step 1: Since 777 > 490, we apply the division lemma to 777 and 490, to get

777 = 490 x 1 + 287

Step 2: Since the reminder 490 ≠ 0, we apply division lemma to 287 and 490, to get

490 = 287 x 1 + 203

Step 3: We consider the new divisor 287 and the new remainder 203, and apply the division lemma to get

287 = 203 x 1 + 84

We consider the new divisor 203 and the new remainder 84,and apply the division lemma to get

203 = 84 x 2 + 35

We consider the new divisor 84 and the new remainder 35,and apply the division lemma to get

84 = 35 x 2 + 14

We consider the new divisor 35 and the new remainder 14,and apply the division lemma to get

35 = 14 x 2 + 7

We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get

14 = 7 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 490 and 777 is 7

Notice that 7 = HCF(14,7) = HCF(35,14) = HCF(84,35) = HCF(203,84) = HCF(287,203) = HCF(490,287) = HCF(777,490) .

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

Step 1: Since 767 > 7, we apply the division lemma to 767 and 7, to get

767 = 7 x 109 + 4

Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 4 and 7, to get

7 = 4 x 1 + 3

Step 3: We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 767 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(767,7) .

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Frequently Asked Questions on HCF of 490, 777, 767 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 490, 777, 767?

Answer: HCF of 490, 777, 767 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 490, 777, 767 using Euclid's Algorithm?

Answer: For arbitrary numbers 490, 777, 767 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.