Highest Common Factor of 309, 532, 714 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 309, 532, 714 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 309, 532, 714 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 309, 532, 714 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 309, 532, 714 is 1.

HCF(309, 532, 714) = 1

HCF of 309, 532, 714 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 309, 532, 714 is 1.

Highest Common Factor of 309,532,714 using Euclid's algorithm

Highest Common Factor of 309,532,714 is 1

Step 1: Since 532 > 309, we apply the division lemma to 532 and 309, to get

532 = 309 x 1 + 223

Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 223 and 309, to get

309 = 223 x 1 + 86

Step 3: We consider the new divisor 223 and the new remainder 86, and apply the division lemma to get

223 = 86 x 2 + 51

We consider the new divisor 86 and the new remainder 51,and apply the division lemma to get

86 = 51 x 1 + 35

We consider the new divisor 51 and the new remainder 35,and apply the division lemma to get

51 = 35 x 1 + 16

We consider the new divisor 35 and the new remainder 16,and apply the division lemma to get

35 = 16 x 2 + 3

We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get

16 = 3 x 5 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 309 and 532 is 1

Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(35,16) = HCF(51,35) = HCF(86,51) = HCF(223,86) = HCF(309,223) = HCF(532,309) .

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

Step 1: Since 714 > 1, we apply the division lemma to 714 and 1, to get

714 = 1 x 714 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 714 is 1

Notice that 1 = HCF(714,1) .

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Frequently Asked Questions on HCF of 309, 532, 714 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 309, 532, 714?

Answer: HCF of 309, 532, 714 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 309, 532, 714 using Euclid's Algorithm?

Answer: For arbitrary numbers 309, 532, 714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.