# Highest Common Factor of 130, 120, 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, 120, 585 i.e. 5 the largest integer that leaves a remainder zero for all numbers.

HCF of 130, 120, 585 is 5 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, 120, 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, 120, 585 is 5.

HCF(130, 120, 585) = 5

## HCF of 130, 120, 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, 120, 585 is 5. ### Highest Common Factor of 130,120,585 is 5

Step 1: Since 130 > 120, we apply the division lemma to 130 and 120, to get

130 = 120 x 1 + 10

Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 10 and 120, to get

120 = 10 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 130 and 120 is 10

Notice that 10 = HCF(120,10) = HCF(130,120) .

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

Step 1: Since 585 > 10, we apply the division lemma to 585 and 10, to get

585 = 10 x 58 + 5

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 5 and 10, to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 10 and 585 is 5

Notice that 5 = HCF(10,5) = HCF(585,10) .

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### Frequently Asked Questions on HCF of 130, 120, 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, 120, 585?

Answer: HCF of 130, 120, 585 is 5 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 130, 120, 585 using Euclid's Algorithm?

Answer: For arbitrary numbers 130, 120, 585 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.