Highest Common Factor of 480, 314, 221, 350 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 480, 314, 221, 350 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 480, 314, 221, 350 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 480, 314, 221, 350 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 480, 314, 221, 350 is 1.

HCF(480, 314, 221, 350) = 1

HCF of 480, 314, 221, 350 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 480, 314, 221, 350 is 1.

Highest Common Factor of 480,314,221,350 using Euclid's algorithm

Highest Common Factor of 480,314,221,350 is 1

Step 1: Since 480 > 314, we apply the division lemma to 480 and 314, to get

480 = 314 x 1 + 166

Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 166 and 314, to get

314 = 166 x 1 + 148

Step 3: We consider the new divisor 166 and the new remainder 148, and apply the division lemma to get

166 = 148 x 1 + 18

We consider the new divisor 148 and the new remainder 18,and apply the division lemma to get

148 = 18 x 8 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 2

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 480 and 314 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(148,18) = HCF(166,148) = HCF(314,166) = HCF(480,314) .

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

Step 1: Since 221 > 2, we apply the division lemma to 221 and 2, to get

221 = 2 x 110 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 221 is 1

Notice that 1 = HCF(2,1) = HCF(221,2) .

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

Step 1: Since 350 > 1, we apply the division lemma to 350 and 1, to get

350 = 1 x 350 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 350 is 1

Notice that 1 = HCF(350,1) .

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Frequently Asked Questions on HCF of 480, 314, 221, 350 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 480, 314, 221, 350?

Answer: HCF of 480, 314, 221, 350 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 480, 314, 221, 350 using Euclid's Algorithm?

Answer: For arbitrary numbers 480, 314, 221, 350 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.