Highest Common Factor of 628, 998, 568 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 628, 998, 568 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 628, 998, 568 is 2 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 628, 998, 568 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 628, 998, 568 is 2.

HCF(628, 998, 568) = 2

HCF of 628, 998, 568 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 628, 998, 568 is 2.

Highest Common Factor of 628,998,568 using Euclid's algorithm

Highest Common Factor of 628,998,568 is 2

Step 1: Since 998 > 628, we apply the division lemma to 998 and 628, to get

998 = 628 x 1 + 370

Step 2: Since the reminder 628 ≠ 0, we apply division lemma to 370 and 628, to get

628 = 370 x 1 + 258

Step 3: We consider the new divisor 370 and the new remainder 258, and apply the division lemma to get

370 = 258 x 1 + 112

We consider the new divisor 258 and the new remainder 112,and apply the division lemma to get

258 = 112 x 2 + 34

We consider the new divisor 112 and the new remainder 34,and apply the division lemma to get

112 = 34 x 3 + 10

We consider the new divisor 34 and the new remainder 10,and apply the division lemma to get

34 = 10 x 3 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 628 and 998 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(34,10) = HCF(112,34) = HCF(258,112) = HCF(370,258) = HCF(628,370) = HCF(998,628) .

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

Step 1: Since 568 > 2, we apply the division lemma to 568 and 2, to get

568 = 2 x 284 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 568 is 2

Notice that 2 = HCF(568,2) .

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Frequently Asked Questions on HCF of 628, 998, 568 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 628, 998, 568?

Answer: HCF of 628, 998, 568 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 628, 998, 568 using Euclid's Algorithm?

Answer: For arbitrary numbers 628, 998, 568 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.