Highest Common Factor of 682, 448, 55 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 682, 448, 55 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 682, 448, 55 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 682, 448, 55 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 682, 448, 55 is 1.

HCF(682, 448, 55) = 1

HCF of 682, 448, 55 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 682, 448, 55 is 1.

Highest Common Factor of 682,448,55 using Euclid's algorithm

Highest Common Factor of 682,448,55 is 1

Step 1: Since 682 > 448, we apply the division lemma to 682 and 448, to get

682 = 448 x 1 + 234

Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 234 and 448, to get

448 = 234 x 1 + 214

Step 3: We consider the new divisor 234 and the new remainder 214, and apply the division lemma to get

234 = 214 x 1 + 20

We consider the new divisor 214 and the new remainder 20,and apply the division lemma to get

214 = 20 x 10 + 14

We consider the new divisor 20 and the new remainder 14,and apply the division lemma to get

20 = 14 x 1 + 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 682 and 448 is 2

Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(20,14) = HCF(214,20) = HCF(234,214) = HCF(448,234) = HCF(682,448) .

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

Step 1: Since 55 > 2, we apply the division lemma to 55 and 2, to get

55 = 2 x 27 + 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 55 is 1

Notice that 1 = HCF(2,1) = HCF(55,2) .

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Frequently Asked Questions on HCF of 682, 448, 55 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 682, 448, 55?

Answer: HCF of 682, 448, 55 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 682, 448, 55 using Euclid's Algorithm?

Answer: For arbitrary numbers 682, 448, 55 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.