Highest Common Factor of 588, 223, 678 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 588, 223, 678 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 588, 223, 678 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 588, 223, 678 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 588, 223, 678 is 1.

HCF(588, 223, 678) = 1

HCF of 588, 223, 678 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 588, 223, 678 is 1.

Highest Common Factor of 588,223,678 using Euclid's algorithm

Highest Common Factor of 588,223,678 is 1

Step 1: Since 588 > 223, we apply the division lemma to 588 and 223, to get

588 = 223 x 2 + 142

Step 2: Since the reminder 223 ≠ 0, we apply division lemma to 142 and 223, to get

223 = 142 x 1 + 81

Step 3: We consider the new divisor 142 and the new remainder 81, and apply the division lemma to get

142 = 81 x 1 + 61

We consider the new divisor 81 and the new remainder 61,and apply the division lemma to get

81 = 61 x 1 + 20

We consider the new divisor 61 and the new remainder 20,and apply the division lemma to get

61 = 20 x 3 + 1

We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get

20 = 1 x 20 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 588 and 223 is 1

Notice that 1 = HCF(20,1) = HCF(61,20) = HCF(81,61) = HCF(142,81) = HCF(223,142) = HCF(588,223) .

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

Step 1: Since 678 > 1, we apply the division lemma to 678 and 1, to get

678 = 1 x 678 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 678 is 1

Notice that 1 = HCF(678,1) .

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Frequently Asked Questions on HCF of 588, 223, 678 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 588, 223, 678?

Answer: HCF of 588, 223, 678 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 588, 223, 678 using Euclid's Algorithm?

Answer: For arbitrary numbers 588, 223, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.