Highest Common Factor of 412, 975, 579 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 412, 975, 579 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 412, 975, 579 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 412, 975, 579 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 412, 975, 579 is 1.

HCF(412, 975, 579) = 1

HCF of 412, 975, 579 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 412, 975, 579 is 1.

Highest Common Factor of 412,975,579 using Euclid's algorithm

Highest Common Factor of 412,975,579 is 1

Step 1: Since 975 > 412, we apply the division lemma to 975 and 412, to get

975 = 412 x 2 + 151

Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 151 and 412, to get

412 = 151 x 2 + 110

Step 3: We consider the new divisor 151 and the new remainder 110, and apply the division lemma to get

151 = 110 x 1 + 41

We consider the new divisor 110 and the new remainder 41,and apply the division lemma to get

110 = 41 x 2 + 28

We consider the new divisor 41 and the new remainder 28,and apply the division lemma to get

41 = 28 x 1 + 13

We consider the new divisor 28 and the new remainder 13,and apply the division lemma to get

28 = 13 x 2 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 412 and 975 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(28,13) = HCF(41,28) = HCF(110,41) = HCF(151,110) = HCF(412,151) = HCF(975,412) .

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

Step 1: Since 579 > 1, we apply the division lemma to 579 and 1, to get

579 = 1 x 579 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 579 is 1

Notice that 1 = HCF(579,1) .

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Frequently Asked Questions on HCF of 412, 975, 579 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 412, 975, 579?

Answer: HCF of 412, 975, 579 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 412, 975, 579 using Euclid's Algorithm?

Answer: For arbitrary numbers 412, 975, 579 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.