Highest Common Factor of 133, 285 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 133, 285 i.e. 19 the largest integer that leaves a remainder zero for all numbers.

HCF of 133, 285 is 19 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 133, 285 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 133, 285 is 19.

HCF(133, 285) = 19

HCF of 133, 285 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 133, 285 is 19.

Highest Common Factor of 133,285 using Euclid's algorithm

Highest Common Factor of 133,285 is 19

Step 1: Since 285 > 133, we apply the division lemma to 285 and 133, to get

285 = 133 x 2 + 19

Step 2: Since the reminder 133 ≠ 0, we apply division lemma to 19 and 133, to get

133 = 19 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 19, the HCF of 133 and 285 is 19

Notice that 19 = HCF(133,19) = HCF(285,133) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 133, 285 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 133, 285?

Answer: HCF of 133, 285 is 19 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 133, 285 using Euclid's Algorithm?

Answer: For arbitrary numbers 133, 285 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.