Highest Common Factor of 7313, 7460, 61678 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 7313, 7460, 61678 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7313, 7460, 61678 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 7313, 7460, 61678 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 7313, 7460, 61678 is 1.

HCF(7313, 7460, 61678) = 1

HCF of 7313, 7460, 61678 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 7313, 7460, 61678 is 1.

Highest Common Factor of 7313,7460,61678 using Euclid's algorithm

Highest Common Factor of 7313,7460,61678 is 1

Step 1: Since 7460 > 7313, we apply the division lemma to 7460 and 7313, to get

7460 = 7313 x 1 + 147

Step 2: Since the reminder 7313 ≠ 0, we apply division lemma to 147 and 7313, to get

7313 = 147 x 49 + 110

Step 3: We consider the new divisor 147 and the new remainder 110, and apply the division lemma to get

147 = 110 x 1 + 37

We consider the new divisor 110 and the new remainder 37,and apply the division lemma to get

110 = 37 x 2 + 36

We consider the new divisor 37 and the new remainder 36,and apply the division lemma to get

37 = 36 x 1 + 1

We consider the new divisor 36 and the new remainder 1,and apply the division lemma to get

36 = 1 x 36 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7313 and 7460 is 1

Notice that 1 = HCF(36,1) = HCF(37,36) = HCF(110,37) = HCF(147,110) = HCF(7313,147) = HCF(7460,7313) .

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

Step 1: Since 61678 > 1, we apply the division lemma to 61678 and 1, to get

61678 = 1 x 61678 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 61678 is 1

Notice that 1 = HCF(61678,1) .

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Frequently Asked Questions on HCF of 7313, 7460, 61678 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 7313, 7460, 61678?

Answer: HCF of 7313, 7460, 61678 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7313, 7460, 61678 using Euclid's Algorithm?

Answer: For arbitrary numbers 7313, 7460, 61678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.