Highest Common Factor of 470, 161, 878, 378 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 470, 161, 878, 378 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 470, 161, 878, 378 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 470, 161, 878, 378 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 470, 161, 878, 378 is 1.

HCF(470, 161, 878, 378) = 1

HCF of 470, 161, 878, 378 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 470, 161, 878, 378 is 1.

Highest Common Factor of 470,161,878,378 using Euclid's algorithm

Highest Common Factor of 470,161,878,378 is 1

Step 1: Since 470 > 161, we apply the division lemma to 470 and 161, to get

470 = 161 x 2 + 148

Step 2: Since the reminder 161 ≠ 0, we apply division lemma to 148 and 161, to get

161 = 148 x 1 + 13

Step 3: We consider the new divisor 148 and the new remainder 13, and apply the division lemma to get

148 = 13 x 11 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 470 and 161 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(148,13) = HCF(161,148) = HCF(470,161) .

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

Step 1: Since 878 > 1, we apply the division lemma to 878 and 1, to get

878 = 1 x 878 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 878 is 1

Notice that 1 = HCF(878,1) .

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

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

378 = 1 x 378 + 0

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

Notice that 1 = HCF(378,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 470, 161, 878, 378 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 470, 161, 878, 378?

Answer: HCF of 470, 161, 878, 378 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 470, 161, 878, 378 using Euclid's Algorithm?

Answer: For arbitrary numbers 470, 161, 878, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.