Highest Common Factor of 578, 997 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 578, 997 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 578, 997 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 578, 997 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 578, 997 is 1.

HCF(578, 997) = 1

HCF of 578, 997 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 578, 997 is 1.

Highest Common Factor of 578,997 using Euclid's algorithm

Highest Common Factor of 578,997 is 1

Step 1: Since 997 > 578, we apply the division lemma to 997 and 578, to get

997 = 578 x 1 + 419

Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 419 and 578, to get

578 = 419 x 1 + 159

Step 3: We consider the new divisor 419 and the new remainder 159, and apply the division lemma to get

419 = 159 x 2 + 101

We consider the new divisor 159 and the new remainder 101,and apply the division lemma to get

159 = 101 x 1 + 58

We consider the new divisor 101 and the new remainder 58,and apply the division lemma to get

101 = 58 x 1 + 43

We consider the new divisor 58 and the new remainder 43,and apply the division lemma to get

58 = 43 x 1 + 15

We consider the new divisor 43 and the new remainder 15,and apply the division lemma to get

43 = 15 x 2 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 578 and 997 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(43,15) = HCF(58,43) = HCF(101,58) = HCF(159,101) = HCF(419,159) = HCF(578,419) = HCF(997,578) .

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Frequently Asked Questions on HCF of 578, 997 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 578, 997?

Answer: HCF of 578, 997 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 578, 997 using Euclid's Algorithm?

Answer: For arbitrary numbers 578, 997 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.