# Highest Common Factor of 40, 80, 120 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 40, 80, 120 i.e. 40 the largest integer that leaves a remainder zero for all numbers.

HCF of 40, 80, 120 is 40 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 40, 80, 120 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 40, 80, 120 is 40.

HCF(40, 80, 120) = 40

## HCF of 40, 80, 120 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 40, 80, 120 is 40. ### Highest Common Factor of 40,80,120 is 40

Step 1: Since 80 > 40, we apply the division lemma to 80 and 40, to get

80 = 40 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 40 and 80 is 40

Notice that 40 = HCF(80,40) .

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

Step 1: Since 120 > 40, we apply the division lemma to 120 and 40, to get

120 = 40 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 40, the HCF of 40 and 120 is 40

Notice that 40 = HCF(120,40) .

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### Frequently Asked Questions on HCF of 40, 80, 120 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 40, 80, 120?

Answer: HCF of 40, 80, 120 is 40 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 40, 80, 120 using Euclid's Algorithm?

Answer: For arbitrary numbers 40, 80, 120 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.