Highest Common Factor of 130, 585 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 130, 585 i.e. 65 the largest integer that leaves a remainder zero for all numbers.

HCF of 130, 585 is 65 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 130, 585 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 130, 585 is 65.

HCF(130, 585) = 65

HCF of 130, 585 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 130, 585 is 65.

Highest Common Factor of 130,585 using Euclid's algorithm

Highest Common Factor of 130,585 is 65

Step 1: Since 585 > 130, we apply the division lemma to 585 and 130, to get

585 = 130 x 4 + 65

Step 2: Since the reminder 130 ≠ 0, we apply division lemma to 65 and 130, to get

130 = 65 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 65, the HCF of 130 and 585 is 65

Notice that 65 = HCF(130,65) = HCF(585,130) .

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Frequently Asked Questions on HCF of 130, 585 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 130, 585?

Answer: HCF of 130, 585 is 65 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 130, 585 using Euclid's Algorithm?

Answer: For arbitrary numbers 130, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.