Highest Common Factor of 420, 730, 311 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, 730, 311 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 420, 730, 311 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, 730, 311 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, 730, 311 is 1.

HCF(420, 730, 311) = 1

HCF of 420, 730, 311 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, 730, 311 is 1.

Highest Common Factor of 420,730,311 using Euclid's algorithm

Highest Common Factor of 420,730,311 is 1

Step 1: Since 730 > 420, we apply the division lemma to 730 and 420, to get

730 = 420 x 1 + 310

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 310 and 420, to get

420 = 310 x 1 + 110

Step 3: We consider the new divisor 310 and the new remainder 110, and apply the division lemma to get

310 = 110 x 2 + 90

We consider the new divisor 110 and the new remainder 90,and apply the division lemma to get

110 = 90 x 1 + 20

We consider the new divisor 90 and the new remainder 20,and apply the division lemma to get

90 = 20 x 4 + 10

We consider the new divisor 20 and the new remainder 10,and apply the division lemma to get

20 = 10 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 420 and 730 is 10

Notice that 10 = HCF(20,10) = HCF(90,20) = HCF(110,90) = HCF(310,110) = HCF(420,310) = HCF(730,420) .

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

Step 1: Since 311 > 10, we apply the division lemma to 311 and 10, to get

311 = 10 x 31 + 1

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 1 and 10, to get

10 = 1 x 10 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 10 and 311 is 1

Notice that 1 = HCF(10,1) = HCF(311,10) .

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Frequently Asked Questions on HCF of 420, 730, 311 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, 730, 311?

Answer: HCF of 420, 730, 311 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 420, 730, 311 using Euclid's Algorithm?

Answer: For arbitrary numbers 420, 730, 311 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.