Highest Common Factor of 7640, 7719, 70774 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 7640, 7719, 70774 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7640, 7719, 70774 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 7640, 7719, 70774 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 7640, 7719, 70774 is 1.

HCF(7640, 7719, 70774) = 1

HCF of 7640, 7719, 70774 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 7640, 7719, 70774 is 1.

Highest Common Factor of 7640,7719,70774 using Euclid's algorithm

Highest Common Factor of 7640,7719,70774 is 1

Step 1: Since 7719 > 7640, we apply the division lemma to 7719 and 7640, to get

7719 = 7640 x 1 + 79

Step 2: Since the reminder 7640 ≠ 0, we apply division lemma to 79 and 7640, to get

7640 = 79 x 96 + 56

Step 3: We consider the new divisor 79 and the new remainder 56, and apply the division lemma to get

79 = 56 x 1 + 23

We consider the new divisor 56 and the new remainder 23,and apply the division lemma to get

56 = 23 x 2 + 10

We consider the new divisor 23 and the new remainder 10,and apply the division lemma to get

23 = 10 x 2 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 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 7640 and 7719 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(23,10) = HCF(56,23) = HCF(79,56) = HCF(7640,79) = HCF(7719,7640) .

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

Step 1: Since 70774 > 1, we apply the division lemma to 70774 and 1, to get

70774 = 1 x 70774 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 70774 is 1

Notice that 1 = HCF(70774,1) .

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Frequently Asked Questions on HCF of 7640, 7719, 70774 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 7640, 7719, 70774?

Answer: HCF of 7640, 7719, 70774 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7640, 7719, 70774 using Euclid's Algorithm?

Answer: For arbitrary numbers 7640, 7719, 70774 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.