Highest Common Factor of 996, 614, 134 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 996, 614, 134 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 996, 614, 134 is 2 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 996, 614, 134 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 996, 614, 134 is 2.

HCF(996, 614, 134) = 2

HCF of 996, 614, 134 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 996, 614, 134 is 2.

Highest Common Factor of 996,614,134 using Euclid's algorithm

Highest Common Factor of 996,614,134 is 2

Step 1: Since 996 > 614, we apply the division lemma to 996 and 614, to get

996 = 614 x 1 + 382

Step 2: Since the reminder 614 ≠ 0, we apply division lemma to 382 and 614, to get

614 = 382 x 1 + 232

Step 3: We consider the new divisor 382 and the new remainder 232, and apply the division lemma to get

382 = 232 x 1 + 150

We consider the new divisor 232 and the new remainder 150,and apply the division lemma to get

232 = 150 x 1 + 82

We consider the new divisor 150 and the new remainder 82,and apply the division lemma to get

150 = 82 x 1 + 68

We consider the new divisor 82 and the new remainder 68,and apply the division lemma to get

82 = 68 x 1 + 14

We consider the new divisor 68 and the new remainder 14,and apply the division lemma to get

68 = 14 x 4 + 12

We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get

14 = 12 x 1 + 2

We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get

12 = 2 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 996 and 614 is 2

Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(68,14) = HCF(82,68) = HCF(150,82) = HCF(232,150) = HCF(382,232) = HCF(614,382) = HCF(996,614) .

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

Step 1: Since 134 > 2, we apply the division lemma to 134 and 2, to get

134 = 2 x 67 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 134 is 2

Notice that 2 = HCF(134,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 996, 614, 134 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 996, 614, 134?

Answer: HCF of 996, 614, 134 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 996, 614, 134 using Euclid's Algorithm?

Answer: For arbitrary numbers 996, 614, 134 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.