Highest Common Factor of 378, 646, 245 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, 646, 245 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 378, 646, 245 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, 646, 245 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, 646, 245 is 1.

HCF(378, 646, 245) = 1

HCF of 378, 646, 245 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, 646, 245 is 1.

Highest Common Factor of 378,646,245 using Euclid's algorithm

Highest Common Factor of 378,646,245 is 1

Step 1: Since 646 > 378, we apply the division lemma to 646 and 378, to get

646 = 378 x 1 + 268

Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 268 and 378, to get

378 = 268 x 1 + 110

Step 3: We consider the new divisor 268 and the new remainder 110, and apply the division lemma to get

268 = 110 x 2 + 48

We consider the new divisor 110 and the new remainder 48,and apply the division lemma to get

110 = 48 x 2 + 14

We consider the new divisor 48 and the new remainder 14,and apply the division lemma to get

48 = 14 x 3 + 6

We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get

14 = 6 x 2 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 378 and 646 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(48,14) = HCF(110,48) = HCF(268,110) = HCF(378,268) = HCF(646,378) .

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

Step 1: Since 245 > 2, we apply the division lemma to 245 and 2, to get

245 = 2 x 122 + 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 245 is 1

Notice that 1 = HCF(2,1) = HCF(245,2) .

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Frequently Asked Questions on HCF of 378, 646, 245 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, 646, 245?

Answer: HCF of 378, 646, 245 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 378, 646, 245 using Euclid's Algorithm?

Answer: For arbitrary numbers 378, 646, 245 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.