Highest Common Factor of 294, 459, 211, 972 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 294, 459, 211, 972 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 294, 459, 211, 972 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 294, 459, 211, 972 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 294, 459, 211, 972 is 1.

HCF(294, 459, 211, 972) = 1

HCF of 294, 459, 211, 972 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 294, 459, 211, 972 is 1.

Highest Common Factor of 294,459,211,972 using Euclid's algorithm

Highest Common Factor of 294,459,211,972 is 1

Step 1: Since 459 > 294, we apply the division lemma to 459 and 294, to get

459 = 294 x 1 + 165

Step 2: Since the reminder 294 ≠ 0, we apply division lemma to 165 and 294, to get

294 = 165 x 1 + 129

Step 3: We consider the new divisor 165 and the new remainder 129, and apply the division lemma to get

165 = 129 x 1 + 36

We consider the new divisor 129 and the new remainder 36,and apply the division lemma to get

129 = 36 x 3 + 21

We consider the new divisor 36 and the new remainder 21,and apply the division lemma to get

36 = 21 x 1 + 15

We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get

21 = 15 x 1 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 294 and 459 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(36,21) = HCF(129,36) = HCF(165,129) = HCF(294,165) = HCF(459,294) .

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

Step 1: Since 211 > 3, we apply the division lemma to 211 and 3, to get

211 = 3 x 70 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 211 is 1

Notice that 1 = HCF(3,1) = HCF(211,3) .

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

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

972 = 1 x 972 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 972 is 1

Notice that 1 = HCF(972,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 294, 459, 211, 972 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 294, 459, 211, 972?

Answer: HCF of 294, 459, 211, 972 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 294, 459, 211, 972 using Euclid's Algorithm?

Answer: For arbitrary numbers 294, 459, 211, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.