Highest Common Factor of 305, 513, 28 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 305, 513, 28 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 305, 513, 28 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 305, 513, 28 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 305, 513, 28 is 1.

HCF(305, 513, 28) = 1

HCF of 305, 513, 28 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 305, 513, 28 is 1.

Highest Common Factor of 305,513,28 using Euclid's algorithm

Highest Common Factor of 305,513,28 is 1

Step 1: Since 513 > 305, we apply the division lemma to 513 and 305, to get

513 = 305 x 1 + 208

Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 208 and 305, to get

305 = 208 x 1 + 97

Step 3: We consider the new divisor 208 and the new remainder 97, and apply the division lemma to get

208 = 97 x 2 + 14

We consider the new divisor 97 and the new remainder 14,and apply the division lemma to get

97 = 14 x 6 + 13

We consider the new divisor 14 and the new remainder 13,and apply the division lemma to get

14 = 13 x 1 + 1

We consider the new divisor 13 and the new remainder 1,and apply the division lemma to get

13 = 1 x 13 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 305 and 513 is 1

Notice that 1 = HCF(13,1) = HCF(14,13) = HCF(97,14) = HCF(208,97) = HCF(305,208) = HCF(513,305) .

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

Step 1: Since 28 > 1, we apply the division lemma to 28 and 1, to get

28 = 1 x 28 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 28 is 1

Notice that 1 = HCF(28,1) .

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Frequently Asked Questions on HCF of 305, 513, 28 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 305, 513, 28?

Answer: HCF of 305, 513, 28 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 305, 513, 28 using Euclid's Algorithm?

Answer: For arbitrary numbers 305, 513, 28 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.