Highest Common Factor of 448, 715, 77 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 448, 715, 77 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 448, 715, 77 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 448, 715, 77 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 448, 715, 77 is 1.

HCF(448, 715, 77) = 1

HCF of 448, 715, 77 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 448, 715, 77 is 1.

Highest Common Factor of 448,715,77 using Euclid's algorithm

Highest Common Factor of 448,715,77 is 1

Step 1: Since 715 > 448, we apply the division lemma to 715 and 448, to get

715 = 448 x 1 + 267

Step 2: Since the reminder 448 ≠ 0, we apply division lemma to 267 and 448, to get

448 = 267 x 1 + 181

Step 3: We consider the new divisor 267 and the new remainder 181, and apply the division lemma to get

267 = 181 x 1 + 86

We consider the new divisor 181 and the new remainder 86,and apply the division lemma to get

181 = 86 x 2 + 9

We consider the new divisor 86 and the new remainder 9,and apply the division lemma to get

86 = 9 x 9 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 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 448 and 715 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(86,9) = HCF(181,86) = HCF(267,181) = HCF(448,267) = HCF(715,448) .

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

Step 1: Since 77 > 1, we apply the division lemma to 77 and 1, to get

77 = 1 x 77 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 77 is 1

Notice that 1 = HCF(77,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 448, 715, 77 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 448, 715, 77?

Answer: HCF of 448, 715, 77 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 448, 715, 77 using Euclid's Algorithm?

Answer: For arbitrary numbers 448, 715, 77 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.