Highest Common Factor of 578, 994, 561 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, 994, 561 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 578, 994, 561 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, 994, 561 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, 994, 561 is 1.

HCF(578, 994, 561) = 1

HCF of 578, 994, 561 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, 994, 561 is 1.

Highest Common Factor of 578,994,561 using Euclid's algorithm

Highest Common Factor of 578,994,561 is 1

Step 1: Since 994 > 578, we apply the division lemma to 994 and 578, to get

994 = 578 x 1 + 416

Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 416 and 578, to get

578 = 416 x 1 + 162

Step 3: We consider the new divisor 416 and the new remainder 162, and apply the division lemma to get

416 = 162 x 2 + 92

We consider the new divisor 162 and the new remainder 92,and apply the division lemma to get

162 = 92 x 1 + 70

We consider the new divisor 92 and the new remainder 70,and apply the division lemma to get

92 = 70 x 1 + 22

We consider the new divisor 70 and the new remainder 22,and apply the division lemma to get

70 = 22 x 3 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 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 578 and 994 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(70,22) = HCF(92,70) = HCF(162,92) = HCF(416,162) = HCF(578,416) = HCF(994,578) .

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

Step 1: Since 561 > 2, we apply the division lemma to 561 and 2, to get

561 = 2 x 280 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 561 is 1

Notice that 1 = HCF(2,1) = HCF(561,2) .

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Frequently Asked Questions on HCF of 578, 994, 561 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, 994, 561?

Answer: HCF of 578, 994, 561 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 578, 994, 561 using Euclid's Algorithm?

Answer: For arbitrary numbers 578, 994, 561 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.