Highest Common Factor of 428, 708, 591 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 428, 708, 591 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 428, 708, 591 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 428, 708, 591 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 428, 708, 591 is 1.

HCF(428, 708, 591) = 1

HCF of 428, 708, 591 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 428, 708, 591 is 1.

Highest Common Factor of 428,708,591 using Euclid's algorithm

Highest Common Factor of 428,708,591 is 1

Step 1: Since 708 > 428, we apply the division lemma to 708 and 428, to get

708 = 428 x 1 + 280

Step 2: Since the reminder 428 ≠ 0, we apply division lemma to 280 and 428, to get

428 = 280 x 1 + 148

Step 3: We consider the new divisor 280 and the new remainder 148, and apply the division lemma to get

280 = 148 x 1 + 132

We consider the new divisor 148 and the new remainder 132,and apply the division lemma to get

148 = 132 x 1 + 16

We consider the new divisor 132 and the new remainder 16,and apply the division lemma to get

132 = 16 x 8 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 428 and 708 is 4

Notice that 4 = HCF(16,4) = HCF(132,16) = HCF(148,132) = HCF(280,148) = HCF(428,280) = HCF(708,428) .

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

Step 1: Since 591 > 4, we apply the division lemma to 591 and 4, to get

591 = 4 x 147 + 3

Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 3 and 4, to get

4 = 3 x 1 + 1

Step 3: 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 4 and 591 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(591,4) .

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Frequently Asked Questions on HCF of 428, 708, 591 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 428, 708, 591?

Answer: HCF of 428, 708, 591 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 428, 708, 591 using Euclid's Algorithm?

Answer: For arbitrary numbers 428, 708, 591 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.