Highest Common Factor of 68, 865, 902 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, 865, 902 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 68, 865, 902 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, 865, 902 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, 865, 902 is 1.

HCF(68, 865, 902) = 1

HCF of 68, 865, 902 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, 865, 902 is 1.

Highest Common Factor of 68,865,902 using Euclid's algorithm

Highest Common Factor of 68,865,902 is 1

Step 1: Since 865 > 68, we apply the division lemma to 865 and 68, to get

865 = 68 x 12 + 49

Step 2: Since the reminder 68 ≠ 0, we apply division lemma to 49 and 68, to get

68 = 49 x 1 + 19

Step 3: We consider the new divisor 49 and the new remainder 19, and apply the division lemma to get

49 = 19 x 2 + 11

We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get

19 = 11 x 1 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 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 68 and 865 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(49,19) = HCF(68,49) = HCF(865,68) .

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

Step 1: Since 902 > 1, we apply the division lemma to 902 and 1, to get

902 = 1 x 902 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 902 is 1

Notice that 1 = HCF(902,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 68, 865, 902 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, 865, 902?

Answer: HCF of 68, 865, 902 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 68, 865, 902 using Euclid's Algorithm?

Answer: For arbitrary numbers 68, 865, 902 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.