# Highest Common Factor of 24, 36, 42 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 24, 36, 42 i.e. 6 the largest integer that leaves a remainder zero for all numbers.

HCF of 24, 36, 42 is 6 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 24, 36, 42 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 24, 36, 42 is 6.

HCF(24, 36, 42) = 6

## HCF of 24, 36, 42 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 24, 36, 42 is 6. ### Highest Common Factor of 24,36,42 is 6

Step 1: Since 36 > 24, we apply the division lemma to 36 and 24, to get

36 = 24 x 1 + 12

Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 12 and 24, to get

24 = 12 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 24 and 36 is 12

Notice that 12 = HCF(24,12) = HCF(36,24) .

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

Step 1: Since 42 > 12, we apply the division lemma to 42 and 12, to get

42 = 12 x 3 + 6

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 6 and 12, to get

12 = 6 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 12 and 42 is 6

Notice that 6 = HCF(12,6) = HCF(42,12) .

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### Frequently Asked Questions on HCF of 24, 36, 42 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 24, 36, 42?

Answer: HCF of 24, 36, 42 is 6 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 24, 36, 42 using Euclid's Algorithm?

Answer: For arbitrary numbers 24, 36, 42 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.