Highest Common Factor of 514, 921, 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 514, 921, 561 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 514, 921, 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 514, 921, 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 514, 921, 561 is 1.

HCF(514, 921, 561) = 1

HCF of 514, 921, 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 514, 921, 561 is 1.

Highest Common Factor of 514,921,561 using Euclid's algorithm

Highest Common Factor of 514,921,561 is 1

Step 1: Since 921 > 514, we apply the division lemma to 921 and 514, to get

921 = 514 x 1 + 407

Step 2: Since the reminder 514 ≠ 0, we apply division lemma to 407 and 514, to get

514 = 407 x 1 + 107

Step 3: We consider the new divisor 407 and the new remainder 107, and apply the division lemma to get

407 = 107 x 3 + 86

We consider the new divisor 107 and the new remainder 86,and apply the division lemma to get

107 = 86 x 1 + 21

We consider the new divisor 86 and the new remainder 21,and apply the division lemma to get

86 = 21 x 4 + 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 514 and 921 is 1

Notice that 1 = HCF(2,1) = HCF(21,2) = HCF(86,21) = HCF(107,86) = HCF(407,107) = HCF(514,407) = HCF(921,514) .

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

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

561 = 1 x 561 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 561 is 1

Notice that 1 = HCF(561,1) .

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Frequently Asked Questions on HCF of 514, 921, 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 514, 921, 561?

Answer: HCF of 514, 921, 561 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 514, 921, 561 using Euclid's Algorithm?

Answer: For arbitrary numbers 514, 921, 561 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.