Highest Common Factor of 828, 577, 126 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 828, 577, 126 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 828, 577, 126 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 828, 577, 126 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 828, 577, 126 is 1.

HCF(828, 577, 126) = 1

HCF of 828, 577, 126 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 828, 577, 126 is 1.

Highest Common Factor of 828,577,126 using Euclid's algorithm

Highest Common Factor of 828,577,126 is 1

Step 1: Since 828 > 577, we apply the division lemma to 828 and 577, to get

828 = 577 x 1 + 251

Step 2: Since the reminder 577 ≠ 0, we apply division lemma to 251 and 577, to get

577 = 251 x 2 + 75

Step 3: We consider the new divisor 251 and the new remainder 75, and apply the division lemma to get

251 = 75 x 3 + 26

We consider the new divisor 75 and the new remainder 26,and apply the division lemma to get

75 = 26 x 2 + 23

We consider the new divisor 26 and the new remainder 23,and apply the division lemma to get

26 = 23 x 1 + 3

We consider the new divisor 23 and the new remainder 3,and apply the division lemma to get

23 = 3 x 7 + 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 828 and 577 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(23,3) = HCF(26,23) = HCF(75,26) = HCF(251,75) = HCF(577,251) = HCF(828,577) .

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

Step 1: Since 126 > 1, we apply the division lemma to 126 and 1, to get

126 = 1 x 126 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 126 is 1

Notice that 1 = HCF(126,1) .

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Frequently Asked Questions on HCF of 828, 577, 126 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 828, 577, 126?

Answer: HCF of 828, 577, 126 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 828, 577, 126 using Euclid's Algorithm?

Answer: For arbitrary numbers 828, 577, 126 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.