Highest Common Factor of 972, 297, 914 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 972, 297, 914 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 972, 297, 914 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 972, 297, 914 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 972, 297, 914 is 1.

HCF(972, 297, 914) = 1

HCF of 972, 297, 914 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 972, 297, 914 is 1.

Highest Common Factor of 972,297,914 using Euclid's algorithm

Highest Common Factor of 972,297,914 is 1

Step 1: Since 972 > 297, we apply the division lemma to 972 and 297, to get

972 = 297 x 3 + 81

Step 2: Since the reminder 297 ≠ 0, we apply division lemma to 81 and 297, to get

297 = 81 x 3 + 54

Step 3: We consider the new divisor 81 and the new remainder 54, and apply the division lemma to get

81 = 54 x 1 + 27

We consider the new divisor 54 and the new remainder 27, and apply the division lemma to get

54 = 27 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 972 and 297 is 27

Notice that 27 = HCF(54,27) = HCF(81,54) = HCF(297,81) = HCF(972,297) .

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

Step 1: Since 914 > 27, we apply the division lemma to 914 and 27, to get

914 = 27 x 33 + 23

Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 23 and 27, to get

27 = 23 x 1 + 4

Step 3: We consider the new divisor 23 and the new remainder 4, and apply the division lemma to get

23 = 4 x 5 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 27 and 914 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(23,4) = HCF(27,23) = HCF(914,27) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 972, 297, 914 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 972, 297, 914?

Answer: HCF of 972, 297, 914 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 972, 297, 914 using Euclid's Algorithm?

Answer: For arbitrary numbers 972, 297, 914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.