Highest Common Factor of 68, 45 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 68, 45 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 68, 45 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 68, 45 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 68, 45 is 1.

HCF(68, 45) = 1

HCF of 68, 45 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 68, 45 is 1.

Highest Common Factor of 68,45 using Euclid's algorithm

Highest Common Factor of 68,45 is 1

Step 1: Since 68 > 45, we apply the division lemma to 68 and 45, to get

68 = 45 x 1 + 23

Step 2: Since the reminder 45 ≠ 0, we apply division lemma to 23 and 45, to get

45 = 23 x 1 + 22

Step 3: We consider the new divisor 23 and the new remainder 22, and apply the division lemma to get

23 = 22 x 1 + 1

We consider the new divisor 22 and the new remainder 1, and apply the division lemma to get

22 = 1 x 22 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 68 and 45 is 1

Notice that 1 = HCF(22,1) = HCF(23,22) = HCF(45,23) = HCF(68,45) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 68, 45 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 68, 45?

Answer: HCF of 68, 45 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 68, 45 using Euclid's Algorithm?

Answer: For arbitrary numbers 68, 45 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.