Highest Common Factor of 305, 528 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, 528 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 305, 528 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, 528 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, 528 is 1.

HCF(305, 528) = 1

HCF of 305, 528 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, 528 is 1.

Highest Common Factor of 305,528 using Euclid's algorithm

Highest Common Factor of 305,528 is 1

Step 1: Since 528 > 305, we apply the division lemma to 528 and 305, to get

528 = 305 x 1 + 223

Step 2: Since the reminder 305 ≠ 0, we apply division lemma to 223 and 305, to get

305 = 223 x 1 + 82

Step 3: We consider the new divisor 223 and the new remainder 82, and apply the division lemma to get

223 = 82 x 2 + 59

We consider the new divisor 82 and the new remainder 59,and apply the division lemma to get

82 = 59 x 1 + 23

We consider the new divisor 59 and the new remainder 23,and apply the division lemma to get

59 = 23 x 2 + 13

We consider the new divisor 23 and the new remainder 13,and apply the division lemma to get

23 = 13 x 1 + 10

We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get

13 = 10 x 1 + 3

We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get

10 = 3 x 3 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 305 and 528 is 1

Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(59,23) = HCF(82,59) = HCF(223,82) = HCF(305,223) = HCF(528,305) .

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Frequently Asked Questions on HCF of 305, 528 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, 528?

Answer: HCF of 305, 528 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 305, 528 using Euclid's Algorithm?

Answer: For arbitrary numbers 305, 528 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.