Highest Common Factor of 478, 784, 158 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 478, 784, 158 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 478, 784, 158 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 478, 784, 158 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 478, 784, 158 is 2.

HCF(478, 784, 158) = 2

HCF of 478, 784, 158 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 478, 784, 158 is 2.

Highest Common Factor of 478,784,158 using Euclid's algorithm

Highest Common Factor of 478,784,158 is 2

Step 1: Since 784 > 478, we apply the division lemma to 784 and 478, to get

784 = 478 x 1 + 306

Step 2: Since the reminder 478 ≠ 0, we apply division lemma to 306 and 478, to get

478 = 306 x 1 + 172

Step 3: We consider the new divisor 306 and the new remainder 172, and apply the division lemma to get

306 = 172 x 1 + 134

We consider the new divisor 172 and the new remainder 134,and apply the division lemma to get

172 = 134 x 1 + 38

We consider the new divisor 134 and the new remainder 38,and apply the division lemma to get

134 = 38 x 3 + 20

We consider the new divisor 38 and the new remainder 20,and apply the division lemma to get

38 = 20 x 1 + 18

We consider the new divisor 20 and the new remainder 18,and apply the division lemma to get

20 = 18 x 1 + 2

We consider the new divisor 18 and the new remainder 2,and apply the division lemma to get

18 = 2 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 478 and 784 is 2

Notice that 2 = HCF(18,2) = HCF(20,18) = HCF(38,20) = HCF(134,38) = HCF(172,134) = HCF(306,172) = HCF(478,306) = HCF(784,478) .

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

Step 1: Since 158 > 2, we apply the division lemma to 158 and 2, to get

158 = 2 x 79 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 158 is 2

Notice that 2 = HCF(158,2) .

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Frequently Asked Questions on HCF of 478, 784, 158 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 478, 784, 158?

Answer: HCF of 478, 784, 158 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 478, 784, 158 using Euclid's Algorithm?

Answer: For arbitrary numbers 478, 784, 158 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.