Highest Common Factor of 120, 150 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 120, 150 i.e. 30 the largest integer that leaves a remainder zero for all numbers.

HCF of 120, 150 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 120, 150 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 120, 150 is 30.

HCF(120, 150) = 30

HCF of 120, 150 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 120, 150 is 30.

Highest Common Factor of 120,150 using Euclid's algorithm

Highest Common Factor of 120,150 is 30

Step 1: Since 150 > 120, we apply the division lemma to 150 and 120, to get

150 = 120 x 1 + 30

Step 2: Since the reminder 120 ≠ 0, we apply division lemma to 30 and 120, to get

120 = 30 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 120 and 150 is 30

Notice that 30 = HCF(120,30) = HCF(150,120) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 120, 150 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 120, 150?

Answer: HCF of 120, 150 is 30 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 120, 150 using Euclid's Algorithm?

Answer: For arbitrary numbers 120, 150 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.