Highest Common Factor of 972, 721, 996 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, 721, 996 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 972, 721, 996 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, 721, 996 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, 721, 996 is 1.

HCF(972, 721, 996) = 1

HCF of 972, 721, 996 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, 721, 996 is 1.

Highest Common Factor of 972,721,996 using Euclid's algorithm

Highest Common Factor of 972,721,996 is 1

Step 1: Since 972 > 721, we apply the division lemma to 972 and 721, to get

972 = 721 x 1 + 251

Step 2: Since the reminder 721 ≠ 0, we apply division lemma to 251 and 721, to get

721 = 251 x 2 + 219

Step 3: We consider the new divisor 251 and the new remainder 219, and apply the division lemma to get

251 = 219 x 1 + 32

We consider the new divisor 219 and the new remainder 32,and apply the division lemma to get

219 = 32 x 6 + 27

We consider the new divisor 32 and the new remainder 27,and apply the division lemma to get

32 = 27 x 1 + 5

We consider the new divisor 27 and the new remainder 5,and apply the division lemma to get

27 = 5 x 5 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 972 and 721 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(27,5) = HCF(32,27) = HCF(219,32) = HCF(251,219) = HCF(721,251) = HCF(972,721) .

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

Step 1: Since 996 > 1, we apply the division lemma to 996 and 1, to get

996 = 1 x 996 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 996 is 1

Notice that 1 = HCF(996,1) .

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Frequently Asked Questions on HCF of 972, 721, 996 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, 721, 996?

Answer: HCF of 972, 721, 996 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 972, 721, 996 using Euclid's Algorithm?

Answer: For arbitrary numbers 972, 721, 996 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.