Highest Common Factor of 285, 914, 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 285, 914, 972 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 285, 914, 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 285, 914, 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 285, 914, 972 is 1.

HCF(285, 914, 972) = 1

HCF of 285, 914, 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 285, 914, 972 is 1.

Highest Common Factor of 285,914,972 using Euclid's algorithm

Highest Common Factor of 285,914,972 is 1

Step 1: Since 914 > 285, we apply the division lemma to 914 and 285, to get

914 = 285 x 3 + 59

Step 2: Since the reminder 285 ≠ 0, we apply division lemma to 59 and 285, to get

285 = 59 x 4 + 49

Step 3: We consider the new divisor 59 and the new remainder 49, and apply the division lemma to get

59 = 49 x 1 + 10

We consider the new divisor 49 and the new remainder 10,and apply the division lemma to get

49 = 10 x 4 + 9

We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get

10 = 9 x 1 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 285 and 914 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(49,10) = HCF(59,49) = HCF(285,59) = HCF(914,285) .

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 285, 914, 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 285, 914, 972?

Answer: HCF of 285, 914, 972 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 285, 914, 972 using Euclid's Algorithm?

Answer: For arbitrary numbers 285, 914, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.