Highest Common Factor of 360, 913, 586, 643 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 360, 913, 586, 643 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 360, 913, 586, 643 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 360, 913, 586, 643 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 360, 913, 586, 643 is 1.

HCF(360, 913, 586, 643) = 1

HCF of 360, 913, 586, 643 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 360, 913, 586, 643 is 1.

Highest Common Factor of 360,913,586,643 using Euclid's algorithm

Highest Common Factor of 360,913,586,643 is 1

Step 1: Since 913 > 360, we apply the division lemma to 913 and 360, to get

913 = 360 x 2 + 193

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 193 and 360, to get

360 = 193 x 1 + 167

Step 3: We consider the new divisor 193 and the new remainder 167, and apply the division lemma to get

193 = 167 x 1 + 26

We consider the new divisor 167 and the new remainder 26,and apply the division lemma to get

167 = 26 x 6 + 11

We consider the new divisor 26 and the new remainder 11,and apply the division lemma to get

26 = 11 x 2 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 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 360 and 913 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(26,11) = HCF(167,26) = HCF(193,167) = HCF(360,193) = HCF(913,360) .

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

Step 1: Since 586 > 1, we apply the division lemma to 586 and 1, to get

586 = 1 x 586 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 586 is 1

Notice that 1 = HCF(586,1) .

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

Step 1: Since 643 > 1, we apply the division lemma to 643 and 1, to get

643 = 1 x 643 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 643 is 1

Notice that 1 = HCF(643,1) .

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Frequently Asked Questions on HCF of 360, 913, 586, 643 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 360, 913, 586, 643?

Answer: HCF of 360, 913, 586, 643 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 360, 913, 586, 643 using Euclid's Algorithm?

Answer: For arbitrary numbers 360, 913, 586, 643 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.