Highest Common Factor of 417, 946 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 417, 946 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 417, 946 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 417, 946 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 417, 946 is 1.

HCF(417, 946) = 1

HCF of 417, 946 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 417, 946 is 1.

Highest Common Factor of 417,946 using Euclid's algorithm

Highest Common Factor of 417,946 is 1

Step 1: Since 946 > 417, we apply the division lemma to 946 and 417, to get

946 = 417 x 2 + 112

Step 2: Since the reminder 417 ≠ 0, we apply division lemma to 112 and 417, to get

417 = 112 x 3 + 81

Step 3: We consider the new divisor 112 and the new remainder 81, and apply the division lemma to get

112 = 81 x 1 + 31

We consider the new divisor 81 and the new remainder 31,and apply the division lemma to get

81 = 31 x 2 + 19

We consider the new divisor 31 and the new remainder 19,and apply the division lemma to get

31 = 19 x 1 + 12

We consider the new divisor 19 and the new remainder 12,and apply the division lemma to get

19 = 12 x 1 + 7

We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get

12 = 7 x 1 + 5

We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get

7 = 5 x 1 + 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 417 and 946 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(31,19) = HCF(81,31) = HCF(112,81) = HCF(417,112) = HCF(946,417) .

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Frequently Asked Questions on HCF of 417, 946 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 417, 946?

Answer: HCF of 417, 946 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 417, 946 using Euclid's Algorithm?

Answer: For arbitrary numbers 417, 946 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.