# Highest Common Factor of 24, 48, 64 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, 48, 64 i.e. 8 the largest integer that leaves a remainder zero for all numbers.

HCF of 24, 48, 64 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 24, 48, 64 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, 48, 64 is 8.

HCF(24, 48, 64) = 8

## HCF of 24, 48, 64 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, 48, 64 is 8. ### Highest Common Factor of 24,48,64 is 8

Step 1: Since 48 > 24, we apply the division lemma to 48 and 24, to get

48 = 24 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 24 and 48 is 24

Notice that 24 = HCF(48,24) .

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

Step 1: Since 64 > 24, we apply the division lemma to 64 and 24, to get

64 = 24 x 2 + 16

Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 16 and 24, to get

24 = 16 x 1 + 8

Step 3: We consider the new divisor 16 and the new remainder 8, and apply the division lemma 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 24 and 64 is 8

Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(64,24) .

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### Frequently Asked Questions on HCF of 24, 48, 64 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, 48, 64?

Answer: HCF of 24, 48, 64 is 8 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 24, 48, 64 using Euclid's Algorithm?

Answer: For arbitrary numbers 24, 48, 64 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.