Highest Common Factor of 946, 412 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 946, 412 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 946, 412 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 946, 412 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 946, 412 is 2.

HCF(946, 412) = 2

HCF of 946, 412 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 946, 412 is 2.

Highest Common Factor of 946,412 using Euclid's algorithm

Highest Common Factor of 946,412 is 2

Step 1: Since 946 > 412, we apply the division lemma to 946 and 412, to get

946 = 412 x 2 + 122

Step 2: Since the reminder 412 ≠ 0, we apply division lemma to 122 and 412, to get

412 = 122 x 3 + 46

Step 3: We consider the new divisor 122 and the new remainder 46, and apply the division lemma to get

122 = 46 x 2 + 30

We consider the new divisor 46 and the new remainder 30,and apply the division lemma to get

46 = 30 x 1 + 16

We consider the new divisor 30 and the new remainder 16,and apply the division lemma to get

30 = 16 x 1 + 14

We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get

16 = 14 x 1 + 2

We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 946 and 412 is 2

Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(30,16) = HCF(46,30) = HCF(122,46) = HCF(412,122) = HCF(946,412) .

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Frequently Asked Questions on HCF of 946, 412 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 946, 412?

Answer: HCF of 946, 412 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 946, 412 using Euclid's Algorithm?

Answer: For arbitrary numbers 946, 412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.