Highest Common Factor of 180, 160 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, 160 i.e. 20 the largest integer that leaves a remainder zero for all numbers.

HCF of 180, 160 is 20 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, 160 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, 160 is 20.

HCF(180, 160) = 20

HCF of 180, 160 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, 160 is 20.

Highest Common Factor of 180,160 using Euclid's algorithm

Highest Common Factor of 180,160 is 20

Step 1: Since 180 > 160, we apply the division lemma to 180 and 160, to get

180 = 160 x 1 + 20

Step 2: Since the reminder 160 ≠ 0, we apply division lemma to 20 and 160, to get

160 = 20 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 180 and 160 is 20

Notice that 20 = HCF(160,20) = HCF(180,160) .

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Frequently Asked Questions on HCF of 180, 160 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, 160?

Answer: HCF of 180, 160 is 20 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 180, 160 using Euclid's Algorithm?

Answer: For arbitrary numbers 180, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.