Highest Common Factor of 307, 3506 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 307, 3506 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 307, 3506 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 307, 3506 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 307, 3506 is 1.

HCF(307, 3506) = 1

HCF of 307, 3506 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 307, 3506 is 1.

Highest Common Factor of 307,3506 using Euclid's algorithm

Highest Common Factor of 307,3506 is 1

Step 1: Since 3506 > 307, we apply the division lemma to 3506 and 307, to get

3506 = 307 x 11 + 129

Step 2: Since the reminder 307 ≠ 0, we apply division lemma to 129 and 307, to get

307 = 129 x 2 + 49

Step 3: We consider the new divisor 129 and the new remainder 49, and apply the division lemma to get

129 = 49 x 2 + 31

We consider the new divisor 49 and the new remainder 31,and apply the division lemma to get

49 = 31 x 1 + 18

We consider the new divisor 31 and the new remainder 18,and apply the division lemma to get

31 = 18 x 1 + 13

We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get

18 = 13 x 1 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 307 and 3506 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(31,18) = HCF(49,31) = HCF(129,49) = HCF(307,129) = HCF(3506,307) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 307, 3506 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 307, 3506?

Answer: HCF of 307, 3506 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 307, 3506 using Euclid's Algorithm?

Answer: For arbitrary numbers 307, 3506 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.