Highest Common Factor of 578, 903, 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, 903, 997 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 578, 903, 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, 903, 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, 903, 997 is 1.

HCF(578, 903, 997) = 1

HCF of 578, 903, 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, 903, 997 is 1.

Highest Common Factor of 578,903,997 using Euclid's algorithm

Highest Common Factor of 578,903,997 is 1

Step 1: Since 903 > 578, we apply the division lemma to 903 and 578, to get

903 = 578 x 1 + 325

Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 325 and 578, to get

578 = 325 x 1 + 253

Step 3: We consider the new divisor 325 and the new remainder 253, and apply the division lemma to get

325 = 253 x 1 + 72

We consider the new divisor 253 and the new remainder 72,and apply the division lemma to get

253 = 72 x 3 + 37

We consider the new divisor 72 and the new remainder 37,and apply the division lemma to get

72 = 37 x 1 + 35

We consider the new divisor 37 and the new remainder 35,and apply the division lemma to get

37 = 35 x 1 + 2

We consider the new divisor 35 and the new remainder 2,and apply the division lemma to get

35 = 2 x 17 + 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 903 is 1

Notice that 1 = HCF(2,1) = HCF(35,2) = HCF(37,35) = HCF(72,37) = HCF(253,72) = HCF(325,253) = HCF(578,325) = HCF(903,578) .

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

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

997 = 1 x 997 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 997 is 1

Notice that 1 = HCF(997,1) .

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Frequently Asked Questions on HCF of 578, 903, 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, 903, 997?

Answer: HCF of 578, 903, 997 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 578, 903, 997 using Euclid's Algorithm?

Answer: For arbitrary numbers 578, 903, 997 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.