Highest Common Factor of 419, 954 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 419, 954 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 419, 954 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 419, 954 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 419, 954 is 1.

HCF(419, 954) = 1

HCF of 419, 954 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 419, 954 is 1.

Highest Common Factor of 419,954 using Euclid's algorithm

Highest Common Factor of 419,954 is 1

Step 1: Since 954 > 419, we apply the division lemma to 954 and 419, to get

954 = 419 x 2 + 116

Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 116 and 419, to get

419 = 116 x 3 + 71

Step 3: We consider the new divisor 116 and the new remainder 71, and apply the division lemma to get

116 = 71 x 1 + 45

We consider the new divisor 71 and the new remainder 45,and apply the division lemma to get

71 = 45 x 1 + 26

We consider the new divisor 45 and the new remainder 26,and apply the division lemma to get

45 = 26 x 1 + 19

We consider the new divisor 26 and the new remainder 19,and apply the division lemma to get

26 = 19 x 1 + 7

We consider the new divisor 19 and the new remainder 7,and apply the division lemma to get

19 = 7 x 2 + 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 419 and 954 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(19,7) = HCF(26,19) = HCF(45,26) = HCF(71,45) = HCF(116,71) = HCF(419,116) = HCF(954,419) .

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Frequently Asked Questions on HCF of 419, 954 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 419, 954?

Answer: HCF of 419, 954 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 419, 954 using Euclid's Algorithm?

Answer: For arbitrary numbers 419, 954 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.