Highest Common Factor of 720, 813, 313 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 720, 813, 313 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 720, 813, 313 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 720, 813, 313 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 720, 813, 313 is 1.

HCF(720, 813, 313) = 1

HCF of 720, 813, 313 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 720, 813, 313 is 1.

Highest Common Factor of 720,813,313 using Euclid's algorithm

Highest Common Factor of 720,813,313 is 1

Step 1: Since 813 > 720, we apply the division lemma to 813 and 720, to get

813 = 720 x 1 + 93

Step 2: Since the reminder 720 ≠ 0, we apply division lemma to 93 and 720, to get

720 = 93 x 7 + 69

Step 3: We consider the new divisor 93 and the new remainder 69, and apply the division lemma to get

93 = 69 x 1 + 24

We consider the new divisor 69 and the new remainder 24,and apply the division lemma to get

69 = 24 x 2 + 21

We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get

24 = 21 x 1 + 3

We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get

21 = 3 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 720 and 813 is 3

Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(69,24) = HCF(93,69) = HCF(720,93) = HCF(813,720) .

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

Step 1: Since 313 > 3, we apply the division lemma to 313 and 3, to get

313 = 3 x 104 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 313 is 1

Notice that 1 = HCF(3,1) = HCF(313,3) .

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Frequently Asked Questions on HCF of 720, 813, 313 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 720, 813, 313?

Answer: HCF of 720, 813, 313 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 720, 813, 313 using Euclid's Algorithm?

Answer: For arbitrary numbers 720, 813, 313 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.