Highest Common Factor of 278, 504, 596 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 278, 504, 596 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 278, 504, 596 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 278, 504, 596 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 278, 504, 596 is 2.

HCF(278, 504, 596) = 2

HCF of 278, 504, 596 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 278, 504, 596 is 2.

Highest Common Factor of 278,504,596 using Euclid's algorithm

Highest Common Factor of 278,504,596 is 2

Step 1: Since 504 > 278, we apply the division lemma to 504 and 278, to get

504 = 278 x 1 + 226

Step 2: Since the reminder 278 ≠ 0, we apply division lemma to 226 and 278, to get

278 = 226 x 1 + 52

Step 3: We consider the new divisor 226 and the new remainder 52, and apply the division lemma to get

226 = 52 x 4 + 18

We consider the new divisor 52 and the new remainder 18,and apply the division lemma to get

52 = 18 x 2 + 16

We consider the new divisor 18 and the new remainder 16,and apply the division lemma to get

18 = 16 x 1 + 2

We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get

16 = 2 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 278 and 504 is 2

Notice that 2 = HCF(16,2) = HCF(18,16) = HCF(52,18) = HCF(226,52) = HCF(278,226) = HCF(504,278) .

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

Step 1: Since 596 > 2, we apply the division lemma to 596 and 2, to get

596 = 2 x 298 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 596 is 2

Notice that 2 = HCF(596,2) .

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Frequently Asked Questions on HCF of 278, 504, 596 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 278, 504, 596?

Answer: HCF of 278, 504, 596 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 278, 504, 596 using Euclid's Algorithm?

Answer: For arbitrary numbers 278, 504, 596 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.