Highest Common Factor of 109, 720, 413 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 109, 720, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 109, 720, 413 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 109, 720, 413 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 109, 720, 413 is 1.

HCF(109, 720, 413) = 1

HCF of 109, 720, 413 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 109, 720, 413 is 1.

Highest Common Factor of 109,720,413 using Euclid's algorithm

Highest Common Factor of 109,720,413 is 1

Step 1: Since 720 > 109, we apply the division lemma to 720 and 109, to get

720 = 109 x 6 + 66

Step 2: Since the reminder 109 ≠ 0, we apply division lemma to 66 and 109, to get

109 = 66 x 1 + 43

Step 3: We consider the new divisor 66 and the new remainder 43, and apply the division lemma to get

66 = 43 x 1 + 23

We consider the new divisor 43 and the new remainder 23,and apply the division lemma to get

43 = 23 x 1 + 20

We consider the new divisor 23 and the new remainder 20,and apply the division lemma to get

23 = 20 x 1 + 3

We consider the new divisor 20 and the new remainder 3,and apply the division lemma to get

20 = 3 x 6 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 109 and 720 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(20,3) = HCF(23,20) = HCF(43,23) = HCF(66,43) = HCF(109,66) = HCF(720,109) .

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

Step 1: Since 413 > 1, we apply the division lemma to 413 and 1, to get

413 = 1 x 413 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 413 is 1

Notice that 1 = HCF(413,1) .

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Frequently Asked Questions on HCF of 109, 720, 413 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 109, 720, 413?

Answer: HCF of 109, 720, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 109, 720, 413 using Euclid's Algorithm?

Answer: For arbitrary numbers 109, 720, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.