# Highest Common Factor of 144, 180, 192 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 144, 180, 192 i.e. 12 the largest integer that leaves a remainder zero for all numbers.

HCF of 144, 180, 192 is 12 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 144, 180, 192 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 144, 180, 192 is 12.

HCF(144, 180, 192) = 12

## HCF of 144, 180, 192 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 144, 180, 192 is 12. ### Highest Common Factor of 144,180,192 is 12

Step 1: Since 180 > 144, we apply the division lemma to 180 and 144, to get

180 = 144 x 1 + 36

Step 2: Since the reminder 144 ≠ 0, we apply division lemma to 36 and 144, to get

144 = 36 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 144 and 180 is 36

Notice that 36 = HCF(144,36) = HCF(180,144) .

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

Step 1: Since 192 > 36, we apply the division lemma to 192 and 36, to get

192 = 36 x 5 + 12

Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 12 and 36, to get

36 = 12 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 36 and 192 is 12

Notice that 12 = HCF(36,12) = HCF(192,36) .

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### Frequently Asked Questions on HCF of 144, 180, 192 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 144, 180, 192?

Answer: HCF of 144, 180, 192 is 12 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 144, 180, 192 using Euclid's Algorithm?

Answer: For arbitrary numbers 144, 180, 192 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.