Highest Common Factor of 378, 587, 257 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 378, 587, 257 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 378, 587, 257 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 378, 587, 257 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 378, 587, 257 is 1.

HCF(378, 587, 257) = 1

HCF of 378, 587, 257 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 378, 587, 257 is 1.

Highest Common Factor of 378,587,257 using Euclid's algorithm

Highest Common Factor of 378,587,257 is 1

Step 1: Since 587 > 378, we apply the division lemma to 587 and 378, to get

587 = 378 x 1 + 209

Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 209 and 378, to get

378 = 209 x 1 + 169

Step 3: We consider the new divisor 209 and the new remainder 169, and apply the division lemma to get

209 = 169 x 1 + 40

We consider the new divisor 169 and the new remainder 40,and apply the division lemma to get

169 = 40 x 4 + 9

We consider the new divisor 40 and the new remainder 9,and apply the division lemma to get

40 = 9 x 4 + 4

We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get

9 = 4 x 2 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 378 and 587 is 1

Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(40,9) = HCF(169,40) = HCF(209,169) = HCF(378,209) = HCF(587,378) .

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

Step 1: Since 257 > 1, we apply the division lemma to 257 and 1, to get

257 = 1 x 257 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 257 is 1

Notice that 1 = HCF(257,1) .

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Frequently Asked Questions on HCF of 378, 587, 257 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 378, 587, 257?

Answer: HCF of 378, 587, 257 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 378, 587, 257 using Euclid's Algorithm?

Answer: For arbitrary numbers 378, 587, 257 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.