Highest Common Factor of 81, 972, 877 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 81, 972, 877 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 81, 972, 877 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 81, 972, 877 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 81, 972, 877 is 1.

HCF(81, 972, 877) = 1

HCF of 81, 972, 877 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 81, 972, 877 is 1.

Highest Common Factor of 81,972,877 using Euclid's algorithm

Highest Common Factor of 81,972,877 is 1

Step 1: Since 972 > 81, we apply the division lemma to 972 and 81, to get

972 = 81 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 81, the HCF of 81 and 972 is 81

Notice that 81 = HCF(972,81) .

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

Step 1: Since 877 > 81, we apply the division lemma to 877 and 81, to get

877 = 81 x 10 + 67

Step 2: Since the reminder 81 ≠ 0, we apply division lemma to 67 and 81, to get

81 = 67 x 1 + 14

Step 3: We consider the new divisor 67 and the new remainder 14, and apply the division lemma to get

67 = 14 x 4 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 81 and 877 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(67,14) = HCF(81,67) = HCF(877,81) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 81, 972, 877 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 81, 972, 877?

Answer: HCF of 81, 972, 877 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 81, 972, 877 using Euclid's Algorithm?

Answer: For arbitrary numbers 81, 972, 877 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.