Highest Common Factor of 683, 126, 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 683, 126, 223 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 683, 126, 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 683, 126, 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 683, 126, 223 is 1.

HCF(683, 126, 223) = 1

HCF of 683, 126, 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 683, 126, 223 is 1.

Highest Common Factor of 683,126,223 using Euclid's algorithm

Highest Common Factor of 683,126,223 is 1

Step 1: Since 683 > 126, we apply the division lemma to 683 and 126, to get

683 = 126 x 5 + 53

Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 53 and 126, to get

126 = 53 x 2 + 20

Step 3: We consider the new divisor 53 and the new remainder 20, and apply the division lemma to get

53 = 20 x 2 + 13

We consider the new divisor 20 and the new remainder 13,and apply the division lemma to get

20 = 13 x 1 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 683 and 126 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(53,20) = HCF(126,53) = HCF(683,126) .

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

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

223 = 1 x 223 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 223 is 1

Notice that 1 = HCF(223,1) .

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Frequently Asked Questions on HCF of 683, 126, 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 683, 126, 223?

Answer: HCF of 683, 126, 223 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 683, 126, 223 using Euclid's Algorithm?

Answer: For arbitrary numbers 683, 126, 223 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.