Highest Common Factor of 51, 74, 66 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 51, 74, 66 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 51, 74, 66 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 51, 74, 66 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 51, 74, 66 is 1.

HCF(51, 74, 66) = 1

HCF of 51, 74, 66 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 51, 74, 66 is 1.

Highest Common Factor of 51,74,66 using Euclid's algorithm

Highest Common Factor of 51,74,66 is 1

Step 1: Since 74 > 51, we apply the division lemma to 74 and 51, to get

74 = 51 x 1 + 23

Step 2: Since the reminder 51 ≠ 0, we apply division lemma to 23 and 51, to get

51 = 23 x 2 + 5

Step 3: We consider the new divisor 23 and the new remainder 5, and apply the division lemma to get

23 = 5 x 4 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 51 and 74 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(23,5) = HCF(51,23) = HCF(74,51) .

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

Step 1: Since 66 > 1, we apply the division lemma to 66 and 1, to get

66 = 1 x 66 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 66 is 1

Notice that 1 = HCF(66,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 51, 74, 66 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 51, 74, 66?

Answer: HCF of 51, 74, 66 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 51, 74, 66 using Euclid's Algorithm?

Answer: For arbitrary numbers 51, 74, 66 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.