Highest Common Factor of 248, 677, 678 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 248, 677, 678 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 248, 677, 678 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 248, 677, 678 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 248, 677, 678 is 1.

HCF(248, 677, 678) = 1

HCF of 248, 677, 678 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 248, 677, 678 is 1.

Highest Common Factor of 248,677,678 using Euclid's algorithm

Highest Common Factor of 248,677,678 is 1

Step 1: Since 677 > 248, we apply the division lemma to 677 and 248, to get

677 = 248 x 2 + 181

Step 2: Since the reminder 248 ≠ 0, we apply division lemma to 181 and 248, to get

248 = 181 x 1 + 67

Step 3: We consider the new divisor 181 and the new remainder 67, and apply the division lemma to get

181 = 67 x 2 + 47

We consider the new divisor 67 and the new remainder 47,and apply the division lemma to get

67 = 47 x 1 + 20

We consider the new divisor 47 and the new remainder 20,and apply the division lemma to get

47 = 20 x 2 + 7

We consider the new divisor 20 and the new remainder 7,and apply the division lemma to get

20 = 7 x 2 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 248 and 677 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(47,20) = HCF(67,47) = HCF(181,67) = HCF(248,181) = HCF(677,248) .

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

Step 1: Since 678 > 1, we apply the division lemma to 678 and 1, to get

678 = 1 x 678 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 678 is 1

Notice that 1 = HCF(678,1) .

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Frequently Asked Questions on HCF of 248, 677, 678 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 248, 677, 678?

Answer: HCF of 248, 677, 678 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 248, 677, 678 using Euclid's Algorithm?

Answer: For arbitrary numbers 248, 677, 678 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.