Highest Common Factor of 825, 612, 392 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 825, 612, 392 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 825, 612, 392 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 825, 612, 392 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 825, 612, 392 is 1.

HCF(825, 612, 392) = 1

HCF of 825, 612, 392 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 825, 612, 392 is 1.

Highest Common Factor of 825,612,392 using Euclid's algorithm

Highest Common Factor of 825,612,392 is 1

Step 1: Since 825 > 612, we apply the division lemma to 825 and 612, to get

825 = 612 x 1 + 213

Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 213 and 612, to get

612 = 213 x 2 + 186

Step 3: We consider the new divisor 213 and the new remainder 186, and apply the division lemma to get

213 = 186 x 1 + 27

We consider the new divisor 186 and the new remainder 27,and apply the division lemma to get

186 = 27 x 6 + 24

We consider the new divisor 27 and the new remainder 24,and apply the division lemma to get

27 = 24 x 1 + 3

We consider the new divisor 24 and the new remainder 3,and apply the division lemma to get

24 = 3 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 825 and 612 is 3

Notice that 3 = HCF(24,3) = HCF(27,24) = HCF(186,27) = HCF(213,186) = HCF(612,213) = HCF(825,612) .

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

Step 1: Since 392 > 3, we apply the division lemma to 392 and 3, to get

392 = 3 x 130 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 392 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(392,3) .

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Frequently Asked Questions on HCF of 825, 612, 392 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 825, 612, 392?

Answer: HCF of 825, 612, 392 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 825, 612, 392 using Euclid's Algorithm?

Answer: For arbitrary numbers 825, 612, 392 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.