Highest Common Factor of 542, 318, 216 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 542, 318, 216 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 542, 318, 216 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 542, 318, 216 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 542, 318, 216 is 2.

HCF(542, 318, 216) = 2

HCF of 542, 318, 216 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 542, 318, 216 is 2.

Highest Common Factor of 542,318,216 using Euclid's algorithm

Highest Common Factor of 542,318,216 is 2

Step 1: Since 542 > 318, we apply the division lemma to 542 and 318, to get

542 = 318 x 1 + 224

Step 2: Since the reminder 318 ≠ 0, we apply division lemma to 224 and 318, to get

318 = 224 x 1 + 94

Step 3: We consider the new divisor 224 and the new remainder 94, and apply the division lemma to get

224 = 94 x 2 + 36

We consider the new divisor 94 and the new remainder 36,and apply the division lemma to get

94 = 36 x 2 + 22

We consider the new divisor 36 and the new remainder 22,and apply the division lemma to get

36 = 22 x 1 + 14

We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get

22 = 14 x 1 + 8

We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get

14 = 8 x 1 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 542 and 318 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(94,36) = HCF(224,94) = HCF(318,224) = HCF(542,318) .

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

Step 1: Since 216 > 2, we apply the division lemma to 216 and 2, to get

216 = 2 x 108 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 216 is 2

Notice that 2 = HCF(216,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 542, 318, 216 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 542, 318, 216?

Answer: HCF of 542, 318, 216 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 542, 318, 216 using Euclid's Algorithm?

Answer: For arbitrary numbers 542, 318, 216 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.