Highest Common Factor of 512, 890, 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 512, 890, 972 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 512, 890, 972 is 2 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 512, 890, 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 512, 890, 972 is 2.

HCF(512, 890, 972) = 2

HCF of 512, 890, 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 512, 890, 972 is 2.

Highest Common Factor of 512,890,972 using Euclid's algorithm

Highest Common Factor of 512,890,972 is 2

Step 1: Since 890 > 512, we apply the division lemma to 890 and 512, to get

890 = 512 x 1 + 378

Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 378 and 512, to get

512 = 378 x 1 + 134

Step 3: We consider the new divisor 378 and the new remainder 134, and apply the division lemma to get

378 = 134 x 2 + 110

We consider the new divisor 134 and the new remainder 110,and apply the division lemma to get

134 = 110 x 1 + 24

We consider the new divisor 110 and the new remainder 24,and apply the division lemma to get

110 = 24 x 4 + 14

We consider the new divisor 24 and the new remainder 14,and apply the division lemma to get

24 = 14 x 1 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 512 and 890 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(24,14) = HCF(110,24) = HCF(134,110) = HCF(378,134) = HCF(512,378) = HCF(890,512) .

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

Step 1: Since 972 > 2, we apply the division lemma to 972 and 2, to get

972 = 2 x 486 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 972 is 2

Notice that 2 = HCF(972,2) .

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Frequently Asked Questions on HCF of 512, 890, 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 512, 890, 972?

Answer: HCF of 512, 890, 972 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 512, 890, 972 using Euclid's Algorithm?

Answer: For arbitrary numbers 512, 890, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.