Highest Common Factor of 972, 556, 581 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, 556, 581 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 972, 556, 581 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, 556, 581 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, 556, 581 is 1.

HCF(972, 556, 581) = 1

HCF of 972, 556, 581 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, 556, 581 is 1.

Highest Common Factor of 972,556,581 using Euclid's algorithm

Highest Common Factor of 972,556,581 is 1

Step 1: Since 972 > 556, we apply the division lemma to 972 and 556, to get

972 = 556 x 1 + 416

Step 2: Since the reminder 556 ≠ 0, we apply division lemma to 416 and 556, to get

556 = 416 x 1 + 140

Step 3: We consider the new divisor 416 and the new remainder 140, and apply the division lemma to get

416 = 140 x 2 + 136

We consider the new divisor 140 and the new remainder 136,and apply the division lemma to get

140 = 136 x 1 + 4

We consider the new divisor 136 and the new remainder 4,and apply the division lemma to get

136 = 4 x 34 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 972 and 556 is 4

Notice that 4 = HCF(136,4) = HCF(140,136) = HCF(416,140) = HCF(556,416) = HCF(972,556) .

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

Step 1: Since 581 > 4, we apply the division lemma to 581 and 4, to get

581 = 4 x 145 + 1

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 581 is 1

Notice that 1 = HCF(4,1) = HCF(581,4) .

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Frequently Asked Questions on HCF of 972, 556, 581 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, 556, 581?

Answer: HCF of 972, 556, 581 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 972, 556, 581 using Euclid's Algorithm?

Answer: For arbitrary numbers 972, 556, 581 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.