Highest Common Factor of 302, 178, 133 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 302, 178, 133 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 302, 178, 133 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 302, 178, 133 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 302, 178, 133 is 1.

HCF(302, 178, 133) = 1

HCF of 302, 178, 133 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 302, 178, 133 is 1.

Highest Common Factor of 302,178,133 using Euclid's algorithm

Highest Common Factor of 302,178,133 is 1

Step 1: Since 302 > 178, we apply the division lemma to 302 and 178, to get

302 = 178 x 1 + 124

Step 2: Since the reminder 178 ≠ 0, we apply division lemma to 124 and 178, to get

178 = 124 x 1 + 54

Step 3: We consider the new divisor 124 and the new remainder 54, and apply the division lemma to get

124 = 54 x 2 + 16

We consider the new divisor 54 and the new remainder 16,and apply the division lemma to get

54 = 16 x 3 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 302 and 178 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(54,16) = HCF(124,54) = HCF(178,124) = HCF(302,178) .

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

Step 1: Since 133 > 2, we apply the division lemma to 133 and 2, to get

133 = 2 x 66 + 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 133 is 1

Notice that 1 = HCF(2,1) = HCF(133,2) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 302, 178, 133 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 302, 178, 133?

Answer: HCF of 302, 178, 133 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 302, 178, 133 using Euclid's Algorithm?

Answer: For arbitrary numbers 302, 178, 133 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.