Highest Common Factor of 714, 530, 223 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 714, 530, 223 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 714, 530, 223 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 714, 530, 223 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 714, 530, 223 is 1.

HCF(714, 530, 223) = 1

HCF of 714, 530, 223 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 714, 530, 223 is 1.

Highest Common Factor of 714,530,223 using Euclid's algorithm

Highest Common Factor of 714,530,223 is 1

Step 1: Since 714 > 530, we apply the division lemma to 714 and 530, to get

714 = 530 x 1 + 184

Step 2: Since the reminder 530 ≠ 0, we apply division lemma to 184 and 530, to get

530 = 184 x 2 + 162

Step 3: We consider the new divisor 184 and the new remainder 162, and apply the division lemma to get

184 = 162 x 1 + 22

We consider the new divisor 162 and the new remainder 22,and apply the division lemma to get

162 = 22 x 7 + 8

We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get

22 = 8 x 2 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 714 and 530 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(162,22) = HCF(184,162) = HCF(530,184) = HCF(714,530) .

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

Step 1: Since 223 > 2, we apply the division lemma to 223 and 2, to get

223 = 2 x 111 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 223 is 1

Notice that 1 = HCF(2,1) = HCF(223,2) .

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Frequently Asked Questions on HCF of 714, 530, 223 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 714, 530, 223?

Answer: HCF of 714, 530, 223 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 714, 530, 223 using Euclid's Algorithm?

Answer: For arbitrary numbers 714, 530, 223 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.