Highest Common Factor of 330, 542, 214 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 330, 542, 214 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 330, 542, 214 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 330, 542, 214 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 330, 542, 214 is 2.

HCF(330, 542, 214) = 2

HCF of 330, 542, 214 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 330, 542, 214 is 2.

Highest Common Factor of 330,542,214 using Euclid's algorithm

Highest Common Factor of 330,542,214 is 2

Step 1: Since 542 > 330, we apply the division lemma to 542 and 330, to get

542 = 330 x 1 + 212

Step 2: Since the reminder 330 ≠ 0, we apply division lemma to 212 and 330, to get

330 = 212 x 1 + 118

Step 3: We consider the new divisor 212 and the new remainder 118, and apply the division lemma to get

212 = 118 x 1 + 94

We consider the new divisor 118 and the new remainder 94,and apply the division lemma to get

118 = 94 x 1 + 24

We consider the new divisor 94 and the new remainder 24,and apply the division lemma to get

94 = 24 x 3 + 22

We consider the new divisor 24 and the new remainder 22,and apply the division lemma to get

24 = 22 x 1 + 2

We consider the new divisor 22 and the new remainder 2,and apply the division lemma to get

22 = 2 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 330 and 542 is 2

Notice that 2 = HCF(22,2) = HCF(24,22) = HCF(94,24) = HCF(118,94) = HCF(212,118) = HCF(330,212) = HCF(542,330) .

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

Step 1: Since 214 > 2, we apply the division lemma to 214 and 2, to get

214 = 2 x 107 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 214 is 2

Notice that 2 = HCF(214,2) .

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Frequently Asked Questions on HCF of 330, 542, 214 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 330, 542, 214?

Answer: HCF of 330, 542, 214 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 330, 542, 214 using Euclid's Algorithm?

Answer: For arbitrary numbers 330, 542, 214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.