Highest Common Factor of 314, 549, 558 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 314, 549, 558 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 314, 549, 558 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 314, 549, 558 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 314, 549, 558 is 1.

HCF(314, 549, 558) = 1

HCF of 314, 549, 558 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 314, 549, 558 is 1.

Highest Common Factor of 314,549,558 using Euclid's algorithm

Highest Common Factor of 314,549,558 is 1

Step 1: Since 549 > 314, we apply the division lemma to 549 and 314, to get

549 = 314 x 1 + 235

Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 235 and 314, to get

314 = 235 x 1 + 79

Step 3: We consider the new divisor 235 and the new remainder 79, and apply the division lemma to get

235 = 79 x 2 + 77

We consider the new divisor 79 and the new remainder 77,and apply the division lemma to get

79 = 77 x 1 + 2

We consider the new divisor 77 and the new remainder 2,and apply the division lemma to get

77 = 2 x 38 + 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 314 and 549 is 1

Notice that 1 = HCF(2,1) = HCF(77,2) = HCF(79,77) = HCF(235,79) = HCF(314,235) = HCF(549,314) .

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

Step 1: Since 558 > 1, we apply the division lemma to 558 and 1, to get

558 = 1 x 558 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 558 is 1

Notice that 1 = HCF(558,1) .

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Frequently Asked Questions on HCF of 314, 549, 558 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 314, 549, 558?

Answer: HCF of 314, 549, 558 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 314, 549, 558 using Euclid's Algorithm?

Answer: For arbitrary numbers 314, 549, 558 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.