Highest Common Factor of 5418, 1988, 33562 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 5418, 1988, 33562 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 5418, 1988, 33562 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 5418, 1988, 33562 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 5418, 1988, 33562 is 2.

HCF(5418, 1988, 33562) = 2

HCF of 5418, 1988, 33562 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 5418, 1988, 33562 is 2.

Highest Common Factor of 5418,1988,33562 using Euclid's algorithm

Highest Common Factor of 5418,1988,33562 is 2

Step 1: Since 5418 > 1988, we apply the division lemma to 5418 and 1988, to get

5418 = 1988 x 2 + 1442

Step 2: Since the reminder 1988 ≠ 0, we apply division lemma to 1442 and 1988, to get

1988 = 1442 x 1 + 546

Step 3: We consider the new divisor 1442 and the new remainder 546, and apply the division lemma to get

1442 = 546 x 2 + 350

We consider the new divisor 546 and the new remainder 350,and apply the division lemma to get

546 = 350 x 1 + 196

We consider the new divisor 350 and the new remainder 196,and apply the division lemma to get

350 = 196 x 1 + 154

We consider the new divisor 196 and the new remainder 154,and apply the division lemma to get

196 = 154 x 1 + 42

We consider the new divisor 154 and the new remainder 42,and apply the division lemma to get

154 = 42 x 3 + 28

We consider the new divisor 42 and the new remainder 28,and apply the division lemma to get

42 = 28 x 1 + 14

We consider the new divisor 28 and the new remainder 14,and apply the division lemma to get

28 = 14 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 5418 and 1988 is 14

Notice that 14 = HCF(28,14) = HCF(42,28) = HCF(154,42) = HCF(196,154) = HCF(350,196) = HCF(546,350) = HCF(1442,546) = HCF(1988,1442) = HCF(5418,1988) .

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

Step 1: Since 33562 > 14, we apply the division lemma to 33562 and 14, to get

33562 = 14 x 2397 + 4

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 4 and 14, to get

14 = 4 x 3 + 2

Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 14 and 33562 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(33562,14) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 5418, 1988, 33562 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 5418, 1988, 33562?

Answer: HCF of 5418, 1988, 33562 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5418, 1988, 33562 using Euclid's Algorithm?

Answer: For arbitrary numbers 5418, 1988, 33562 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.