Highest Common Factor of 345, 527, 228 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, 527, 228 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 345, 527, 228 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 345, 527, 228 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, 527, 228 is 1.

HCF(345, 527, 228) = 1

HCF of 345, 527, 228 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, 527, 228 is 1.

Highest Common Factor of 345,527,228 using Euclid's algorithm

Highest Common Factor of 345,527,228 is 1

Step 1: Since 527 > 345, we apply the division lemma to 527 and 345, to get

527 = 345 x 1 + 182

Step 2: Since the reminder 345 ≠ 0, we apply division lemma to 182 and 345, to get

345 = 182 x 1 + 163

Step 3: We consider the new divisor 182 and the new remainder 163, and apply the division lemma to get

182 = 163 x 1 + 19

We consider the new divisor 163 and the new remainder 19,and apply the division lemma to get

163 = 19 x 8 + 11

We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get

19 = 11 x 1 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 345 and 527 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(163,19) = HCF(182,163) = HCF(345,182) = HCF(527,345) .

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

Step 1: Since 228 > 1, we apply the division lemma to 228 and 1, to get

228 = 1 x 228 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 228 is 1

Notice that 1 = HCF(228,1) .

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Frequently Asked Questions on HCF of 345, 527, 228 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, 527, 228?

Answer: HCF of 345, 527, 228 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 345, 527, 228 using Euclid's Algorithm?

Answer: For arbitrary numbers 345, 527, 228 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.