Highest Common Factor of 432, 278, 278 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 432, 278, 278 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 432, 278, 278 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 432, 278, 278 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 432, 278, 278 is 2.

HCF(432, 278, 278) = 2

HCF of 432, 278, 278 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 432, 278, 278 is 2.

Highest Common Factor of 432,278,278 using Euclid's algorithm

Highest Common Factor of 432,278,278 is 2

Step 1: Since 432 > 278, we apply the division lemma to 432 and 278, to get

432 = 278 x 1 + 154

Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 154 and 278, to get

278 = 154 x 1 + 124

Step 3: We consider the new divisor 154 and the new remainder 124, and apply the division lemma to get

154 = 124 x 1 + 30

We consider the new divisor 124 and the new remainder 30,and apply the division lemma to get

124 = 30 x 4 + 4

We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get

30 = 4 x 7 + 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 432 and 278 is 2

Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(124,30) = HCF(154,124) = HCF(278,154) = HCF(432,278) .

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

Step 1: Since 278 > 2, we apply the division lemma to 278 and 2, to get

278 = 2 x 139 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 278 is 2

Notice that 2 = HCF(278,2) .

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Frequently Asked Questions on HCF of 432, 278, 278 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 432, 278, 278?

Answer: HCF of 432, 278, 278 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 432, 278, 278 using Euclid's Algorithm?

Answer: For arbitrary numbers 432, 278, 278 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.