Highest Common Factor of 345, 528, 54 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 345, 528, 54 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 345, 528, 54 is 3 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 345, 528, 54 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 345, 528, 54 is 3.

HCF(345, 528, 54) = 3

HCF of 345, 528, 54 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 345, 528, 54 is 3.

Highest Common Factor of 345,528,54 using Euclid's algorithm

Highest Common Factor of 345,528,54 is 3

Step 1: Since 528 > 345, we apply the division lemma to 528 and 345, to get

528 = 345 x 1 + 183

Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 183 and 345, to get

345 = 183 x 1 + 162

Step 3: We consider the new divisor 183 and the new remainder 162, and apply the division lemma to get

183 = 162 x 1 + 21

We consider the new divisor 162 and the new remainder 21,and apply the division lemma to get

162 = 21 x 7 + 15

We consider the new divisor 21 and the new remainder 15,and apply the division lemma to get

21 = 15 x 1 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 345 and 528 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(21,15) = HCF(162,21) = HCF(183,162) = HCF(345,183) = HCF(528,345) .

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

Step 1: Since 54 > 3, we apply the division lemma to 54 and 3, to get

54 = 3 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 54 is 3

Notice that 3 = HCF(54,3) .

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Frequently Asked Questions on HCF of 345, 528, 54 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 345, 528, 54?

Answer: HCF of 345, 528, 54 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 345, 528, 54 using Euclid's Algorithm?

Answer: For arbitrary numbers 345, 528, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.