Highest Common Factor of 829, 228, 256 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 829, 228, 256 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 829, 228, 256 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 829, 228, 256 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 829, 228, 256 is 1.

HCF(829, 228, 256) = 1

HCF of 829, 228, 256 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 829, 228, 256 is 1.

Highest Common Factor of 829,228,256 using Euclid's algorithm

Highest Common Factor of 829,228,256 is 1

Step 1: Since 829 > 228, we apply the division lemma to 829 and 228, to get

829 = 228 x 3 + 145

Step 2: Since the reminder 228 ≠ 0, we apply division lemma to 145 and 228, to get

228 = 145 x 1 + 83

Step 3: We consider the new divisor 145 and the new remainder 83, and apply the division lemma to get

145 = 83 x 1 + 62

We consider the new divisor 83 and the new remainder 62,and apply the division lemma to get

83 = 62 x 1 + 21

We consider the new divisor 62 and the new remainder 21,and apply the division lemma to get

62 = 21 x 2 + 20

We consider the new divisor 21 and the new remainder 20,and apply the division lemma to get

21 = 20 x 1 + 1

We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get

20 = 1 x 20 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 829 and 228 is 1

Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(62,21) = HCF(83,62) = HCF(145,83) = HCF(228,145) = HCF(829,228) .

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

Step 1: Since 256 > 1, we apply the division lemma to 256 and 1, to get

256 = 1 x 256 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 256 is 1

Notice that 1 = HCF(256,1) .

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Frequently Asked Questions on HCF of 829, 228, 256 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 829, 228, 256?

Answer: HCF of 829, 228, 256 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 829, 228, 256 using Euclid's Algorithm?

Answer: For arbitrary numbers 829, 228, 256 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.