Highest Common Factor of 307, 222, 509 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, 222, 509 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 307, 222, 509 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, 222, 509 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, 222, 509 is 1.

HCF(307, 222, 509) = 1

HCF of 307, 222, 509 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, 222, 509 is 1.

Highest Common Factor of 307,222,509 using Euclid's algorithm

Highest Common Factor of 307,222,509 is 1

Step 1: Since 307 > 222, we apply the division lemma to 307 and 222, to get

307 = 222 x 1 + 85

Step 2: Since the reminder 222 ≠ 0, we apply division lemma to 85 and 222, to get

222 = 85 x 2 + 52

Step 3: We consider the new divisor 85 and the new remainder 52, and apply the division lemma to get

85 = 52 x 1 + 33

We consider the new divisor 52 and the new remainder 33,and apply the division lemma to get

52 = 33 x 1 + 19

We consider the new divisor 33 and the new remainder 19,and apply the division lemma to get

33 = 19 x 1 + 14

We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get

19 = 14 x 1 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 307 and 222 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(33,19) = HCF(52,33) = HCF(85,52) = HCF(222,85) = HCF(307,222) .

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

Step 1: Since 509 > 1, we apply the division lemma to 509 and 1, to get

509 = 1 x 509 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 509 is 1

Notice that 1 = HCF(509,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 307, 222, 509 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, 222, 509?

Answer: HCF of 307, 222, 509 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 307, 222, 509 using Euclid's Algorithm?

Answer: For arbitrary numbers 307, 222, 509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.