Highest Common Factor of 612, 996, 545 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 612, 996, 545 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 612, 996, 545 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 612, 996, 545 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 612, 996, 545 is 1.

HCF(612, 996, 545) = 1

HCF of 612, 996, 545 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 612, 996, 545 is 1.

Highest Common Factor of 612,996,545 using Euclid's algorithm

Highest Common Factor of 612,996,545 is 1

Step 1: Since 996 > 612, we apply the division lemma to 996 and 612, to get

996 = 612 x 1 + 384

Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 384 and 612, to get

612 = 384 x 1 + 228

Step 3: We consider the new divisor 384 and the new remainder 228, and apply the division lemma to get

384 = 228 x 1 + 156

We consider the new divisor 228 and the new remainder 156,and apply the division lemma to get

228 = 156 x 1 + 72

We consider the new divisor 156 and the new remainder 72,and apply the division lemma to get

156 = 72 x 2 + 12

We consider the new divisor 72 and the new remainder 12,and apply the division lemma to get

72 = 12 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 612 and 996 is 12

Notice that 12 = HCF(72,12) = HCF(156,72) = HCF(228,156) = HCF(384,228) = HCF(612,384) = HCF(996,612) .

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

Step 1: Since 545 > 12, we apply the division lemma to 545 and 12, to get

545 = 12 x 45 + 5

Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 5 and 12, to get

12 = 5 x 2 + 2

Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get

5 = 2 x 2 + 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 12 and 545 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(545,12) .

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Frequently Asked Questions on HCF of 612, 996, 545 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 612, 996, 545?

Answer: HCF of 612, 996, 545 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 612, 996, 545 using Euclid's Algorithm?

Answer: For arbitrary numbers 612, 996, 545 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.