Highest Common Factor of 180, 210 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 180, 210 i.e. 30 the largest integer that leaves a remainder zero for all numbers.

HCF of 180, 210 is 30 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 180, 210 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 180, 210 is 30.

HCF(180, 210) = 30

HCF of 180, 210 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 180, 210 is 30.

Highest Common Factor of 180,210 using Euclid's algorithm

Highest Common Factor of 180,210 is 30

Step 1: Since 210 > 180, we apply the division lemma to 210 and 180, to get

210 = 180 x 1 + 30

Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 30 and 180, to get

180 = 30 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 180 and 210 is 30

Notice that 30 = HCF(180,30) = HCF(210,180) .

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Frequently Asked Questions on HCF of 180, 210 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 180, 210?

Answer: HCF of 180, 210 is 30 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 180, 210 using Euclid's Algorithm?

Answer: For arbitrary numbers 180, 210 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.