# Highest Common Factor of 150, 200, 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 150, 200, 180 i.e. 10 the largest integer that leaves a remainder zero for all numbers.

HCF of 150, 200, 180 is 10 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 150, 200, 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 150, 200, 180 is 10.

HCF(150, 200, 180) = 10

## HCF of 150, 200, 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 150, 200, 180 is 10. ### Highest Common Factor of 150,200,180 is 10

Step 1: Since 200 > 150, we apply the division lemma to 200 and 150, to get

200 = 150 x 1 + 50

Step 2: Since the reminder 150 ≠ 0, we apply division lemma to 50 and 150, to get

150 = 50 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 50, the HCF of 150 and 200 is 50

Notice that 50 = HCF(150,50) = HCF(200,150) .

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

Step 1: Since 180 > 50, we apply the division lemma to 180 and 50, to get

180 = 50 x 3 + 30

Step 2: Since the reminder 50 ≠ 0, we apply division lemma to 30 and 50, to get

50 = 30 x 1 + 20

Step 3: We consider the new divisor 30 and the new remainder 20, and apply the division lemma to get

30 = 20 x 1 + 10

We consider the new divisor 20 and the new remainder 10, and apply the division lemma to get

20 = 10 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 50 and 180 is 10

Notice that 10 = HCF(20,10) = HCF(30,20) = HCF(50,30) = HCF(180,50) .

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### Frequently Asked Questions on HCF of 150, 200, 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 150, 200, 180?

Answer: HCF of 150, 200, 180 is 10 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 150, 200, 180 using Euclid's Algorithm?

Answer: For arbitrary numbers 150, 200, 180 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.