Highest Common Factor of 420, 715, 408 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 420, 715, 408 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 715, 408 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 420, 715, 408 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 420, 715, 408 is 1.

HCF(420, 715, 408) = 1

HCF of 420, 715, 408 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 420, 715, 408 is 1.

Highest Common Factor of 420,715,408 using Euclid's algorithm

Highest Common Factor of 420,715,408 is 1

Step 1: Since 715 > 420, we apply the division lemma to 715 and 420, to get

715 = 420 x 1 + 295

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 295 and 420, to get

420 = 295 x 1 + 125

Step 3: We consider the new divisor 295 and the new remainder 125, and apply the division lemma to get

295 = 125 x 2 + 45

We consider the new divisor 125 and the new remainder 45,and apply the division lemma to get

125 = 45 x 2 + 35

We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get

45 = 35 x 1 + 10

We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get

35 = 10 x 3 + 5

We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get

10 = 5 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 420 and 715 is 5

Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(125,45) = HCF(295,125) = HCF(420,295) = HCF(715,420) .

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

Step 1: Since 408 > 5, we apply the division lemma to 408 and 5, to get

408 = 5 x 81 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: 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 5 and 408 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(408,5) .

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Frequently Asked Questions on HCF of 420, 715, 408 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 420, 715, 408?

Answer: HCF of 420, 715, 408 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 715, 408 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 715, 408 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.