Highest Common Factor of 415, 672, 629 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 415, 672, 629 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 415, 672, 629 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 415, 672, 629 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 415, 672, 629 is 1.

HCF(415, 672, 629) = 1

HCF of 415, 672, 629 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 415, 672, 629 is 1.

Highest Common Factor of 415,672,629 using Euclid's algorithm

Highest Common Factor of 415,672,629 is 1

Step 1: Since 672 > 415, we apply the division lemma to 672 and 415, to get

672 = 415 x 1 + 257

Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 257 and 415, to get

415 = 257 x 1 + 158

Step 3: We consider the new divisor 257 and the new remainder 158, and apply the division lemma to get

257 = 158 x 1 + 99

We consider the new divisor 158 and the new remainder 99,and apply the division lemma to get

158 = 99 x 1 + 59

We consider the new divisor 99 and the new remainder 59,and apply the division lemma to get

99 = 59 x 1 + 40

We consider the new divisor 59 and the new remainder 40,and apply the division lemma to get

59 = 40 x 1 + 19

We consider the new divisor 40 and the new remainder 19,and apply the division lemma to get

40 = 19 x 2 + 2

We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get

19 = 2 x 9 + 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 415 and 672 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(40,19) = HCF(59,40) = HCF(99,59) = HCF(158,99) = HCF(257,158) = HCF(415,257) = HCF(672,415) .

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

Step 1: Since 629 > 1, we apply the division lemma to 629 and 1, to get

629 = 1 x 629 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 629 is 1

Notice that 1 = HCF(629,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 415, 672, 629 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 415, 672, 629?

Answer: HCF of 415, 672, 629 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 415, 672, 629 using Euclid's Algorithm?

Answer: For arbitrary numbers 415, 672, 629 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.