Highest Common Factor of 710, 649, 364 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 710, 649, 364 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 710, 649, 364 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 710, 649, 364 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 710, 649, 364 is 1.

HCF(710, 649, 364) = 1

HCF of 710, 649, 364 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 710, 649, 364 is 1.

Highest Common Factor of 710,649,364 using Euclid's algorithm

Highest Common Factor of 710,649,364 is 1

Step 1: Since 710 > 649, we apply the division lemma to 710 and 649, to get

710 = 649 x 1 + 61

Step 2: Since the reminder 649 ≠ 0, we apply division lemma to 61 and 649, to get

649 = 61 x 10 + 39

Step 3: We consider the new divisor 61 and the new remainder 39, and apply the division lemma to get

61 = 39 x 1 + 22

We consider the new divisor 39 and the new remainder 22,and apply the division lemma to get

39 = 22 x 1 + 17

We consider the new divisor 22 and the new remainder 17,and apply the division lemma to get

22 = 17 x 1 + 5

We consider the new divisor 17 and the new remainder 5,and apply the division lemma to get

17 = 5 x 3 + 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 710 and 649 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(17,5) = HCF(22,17) = HCF(39,22) = HCF(61,39) = HCF(649,61) = HCF(710,649) .

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

Step 1: Since 364 > 1, we apply the division lemma to 364 and 1, to get

364 = 1 x 364 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 364 is 1

Notice that 1 = HCF(364,1) .

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Frequently Asked Questions on HCF of 710, 649, 364 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 710, 649, 364?

Answer: HCF of 710, 649, 364 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 710, 649, 364 using Euclid's Algorithm?

Answer: For arbitrary numbers 710, 649, 364 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.