Highest Common Factor of 412, 712, 826 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, 712, 826 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 412, 712, 826 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 412, 712, 826 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, 712, 826 is 2.

HCF(412, 712, 826) = 2

HCF of 412, 712, 826 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, 712, 826 is 2.

Highest Common Factor of 412,712,826 using Euclid's algorithm

Highest Common Factor of 412,712,826 is 2

Step 1: Since 712 > 412, we apply the division lemma to 712 and 412, to get

712 = 412 x 1 + 300

Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 300 and 412, to get

412 = 300 x 1 + 112

Step 3: We consider the new divisor 300 and the new remainder 112, and apply the division lemma to get

300 = 112 x 2 + 76

We consider the new divisor 112 and the new remainder 76,and apply the division lemma to get

112 = 76 x 1 + 36

We consider the new divisor 76 and the new remainder 36,and apply the division lemma to get

76 = 36 x 2 + 4

We consider the new divisor 36 and the new remainder 4,and apply the division lemma to get

36 = 4 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 412 and 712 is 4

Notice that 4 = HCF(36,4) = HCF(76,36) = HCF(112,76) = HCF(300,112) = HCF(412,300) = HCF(712,412) .

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

Step 1: Since 826 > 4, we apply the division lemma to 826 and 4, to get

826 = 4 x 206 + 2

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 826 is 2

Notice that 2 = HCF(4,2) = HCF(826,4) .

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Frequently Asked Questions on HCF of 412, 712, 826 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, 712, 826?

Answer: HCF of 412, 712, 826 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 412, 712, 826 using Euclid's Algorithm?

Answer: For arbitrary numbers 412, 712, 826 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.