# Highest Common Factor of 36, 105, 180 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 36, 105, 180 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 36, 105, 180 is 3 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 36, 105, 180 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 36, 105, 180 is 3.

HCF(36, 105, 180) = 3

## HCF of 36, 105, 180 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 36, 105, 180 is 3. ### Highest Common Factor of 36,105,180 is 3

Step 1: Since 105 > 36, we apply the division lemma to 105 and 36, to get

105 = 36 x 2 + 33

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 33 and 36, to get

36 = 33 x 1 + 3

Step 3: We consider the new divisor 33 and the new remainder 3, and apply the division lemma to get

33 = 3 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 36 and 105 is 3

Notice that 3 = HCF(33,3) = HCF(36,33) = HCF(105,36) .

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

Step 1: Since 180 > 3, we apply the division lemma to 180 and 3, to get

180 = 3 x 60 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 180 is 3

Notice that 3 = HCF(180,3) .

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### Frequently Asked Questions on HCF of 36, 105, 180 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 36, 105, 180?

Answer: HCF of 36, 105, 180 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 36, 105, 180 using Euclid's Algorithm?

Answer: For arbitrary numbers 36, 105, 180 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.