Highest Common Factor of 415, 983, 564 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 415, 983, 564 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 415, 983, 564 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 415, 983, 564 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 415, 983, 564 is 1.

HCF(415, 983, 564) = 1

HCF of 415, 983, 564 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 415, 983, 564 is 1.

Highest Common Factor of 415,983,564 using Euclid's algorithm

Highest Common Factor of 415,983,564 is 1

Step 1: Since 983 > 415, we apply the division lemma to 983 and 415, to get

983 = 415 x 2 + 153

Step 2: Since the reminder 415 ≠ 0, we apply division lemma to 153 and 415, to get

415 = 153 x 2 + 109

Step 3: We consider the new divisor 153 and the new remainder 109, and apply the division lemma to get

153 = 109 x 1 + 44

We consider the new divisor 109 and the new remainder 44,and apply the division lemma to get

109 = 44 x 2 + 21

We consider the new divisor 44 and the new remainder 21,and apply the division lemma to get

44 = 21 x 2 + 2

We consider the new divisor 21 and the new remainder 2,and apply the division lemma to get

21 = 2 x 10 + 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 415 and 983 is 1

Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(44,21) = HCF(109,44) = HCF(153,109) = HCF(415,153) = HCF(983,415) .

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

Step 1: Since 564 > 1, we apply the division lemma to 564 and 1, to get

564 = 1 x 564 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 564 is 1

Notice that 1 = HCF(564,1) .

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Frequently Asked Questions on HCF of 415, 983, 564 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 415, 983, 564?

Answer: HCF of 415, 983, 564 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 415, 983, 564 using Euclid's Algorithm?

Answer: For arbitrary numbers 415, 983, 564 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.