# Highest Common Factor of 16, 32, 40 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 16, 32, 40 i.e. 8 the largest integer that leaves a remainder zero for all numbers.

HCF of 16, 32, 40 is 8 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 16, 32, 40 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 16, 32, 40 is 8.

HCF(16, 32, 40) = 8

## HCF of 16, 32, 40 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 16, 32, 40 is 8. ### Highest Common Factor of 16,32,40 is 8

Step 1: Since 32 > 16, we apply the division lemma to 32 and 16, to get

32 = 16 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 16 and 32 is 16

Notice that 16 = HCF(32,16) .

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

Step 1: Since 40 > 16, we apply the division lemma to 40 and 16, to get

40 = 16 x 2 + 8

Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 8 and 16, to get

16 = 8 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 16 and 40 is 8

Notice that 8 = HCF(16,8) = HCF(40,16) .

### HCF using Euclid's Algorithm Calculation Examples

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

### Frequently Asked Questions on HCF of 16, 32, 40 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 16, 32, 40?

Answer: HCF of 16, 32, 40 is 8 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 16, 32, 40 using Euclid's Algorithm?

Answer: For arbitrary numbers 16, 32, 40 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.