# Highest Common Factor of 55, 96, 54 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 55, 96, 54 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 55, 96, 54 is 1 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 55, 96, 54 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 55, 96, 54 is 1.

HCF(55, 96, 54) = 1

## HCF of 55, 96, 54 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 55, 96, 54 is 1. ### Highest Common Factor of 55,96,54 is 1

Step 1: Since 96 > 55, we apply the division lemma to 96 and 55, to get

96 = 55 x 1 + 41

Step 2: Since the reminder 55 ≠ 0, we apply division lemma to 41 and 55, to get

55 = 41 x 1 + 14

Step 3: We consider the new divisor 41 and the new remainder 14, and apply the division lemma to get

41 = 14 x 2 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 55 and 96 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(41,14) = HCF(55,41) = HCF(96,55) .

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

Step 1: Since 54 > 1, we apply the division lemma to 54 and 1, to get

54 = 1 x 54 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 54 is 1

Notice that 1 = HCF(54,1) .

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### Frequently Asked Questions on HCF of 55, 96, 54 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 55, 96, 54?

Answer: HCF of 55, 96, 54 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 55, 96, 54 using Euclid's Algorithm?

Answer: For arbitrary numbers 55, 96, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.