Highest Common Factor of 516, 855, 224 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 516, 855, 224 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 516, 855, 224 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 516, 855, 224 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 516, 855, 224 is 1.

HCF(516, 855, 224) = 1

HCF of 516, 855, 224 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 516, 855, 224 is 1.

Highest Common Factor of 516,855,224 using Euclid's algorithm

Highest Common Factor of 516,855,224 is 1

Step 1: Since 855 > 516, we apply the division lemma to 855 and 516, to get

855 = 516 x 1 + 339

Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 339 and 516, to get

516 = 339 x 1 + 177

Step 3: We consider the new divisor 339 and the new remainder 177, and apply the division lemma to get

339 = 177 x 1 + 162

We consider the new divisor 177 and the new remainder 162,and apply the division lemma to get

177 = 162 x 1 + 15

We consider the new divisor 162 and the new remainder 15,and apply the division lemma to get

162 = 15 x 10 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 516 and 855 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(162,15) = HCF(177,162) = HCF(339,177) = HCF(516,339) = HCF(855,516) .

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

Step 1: Since 224 > 3, we apply the division lemma to 224 and 3, to get

224 = 3 x 74 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 224 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(224,3) .

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Frequently Asked Questions on HCF of 516, 855, 224 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 516, 855, 224?

Answer: HCF of 516, 855, 224 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 516, 855, 224 using Euclid's Algorithm?

Answer: For arbitrary numbers 516, 855, 224 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.