Highest Common Factor of 2945, 8167, 20353 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 2945, 8167, 20353 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2945, 8167, 20353 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 2945, 8167, 20353 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 2945, 8167, 20353 is 1.

HCF(2945, 8167, 20353) = 1

HCF of 2945, 8167, 20353 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 2945, 8167, 20353 is 1.

Highest Common Factor of 2945,8167,20353 using Euclid's algorithm

Highest Common Factor of 2945,8167,20353 is 1

Step 1: Since 8167 > 2945, we apply the division lemma to 8167 and 2945, to get

8167 = 2945 x 2 + 2277

Step 2: Since the reminder 2945 ≠ 0, we apply division lemma to 2277 and 2945, to get

2945 = 2277 x 1 + 668

Step 3: We consider the new divisor 2277 and the new remainder 668, and apply the division lemma to get

2277 = 668 x 3 + 273

We consider the new divisor 668 and the new remainder 273,and apply the division lemma to get

668 = 273 x 2 + 122

We consider the new divisor 273 and the new remainder 122,and apply the division lemma to get

273 = 122 x 2 + 29

We consider the new divisor 122 and the new remainder 29,and apply the division lemma to get

122 = 29 x 4 + 6

We consider the new divisor 29 and the new remainder 6,and apply the division lemma to get

29 = 6 x 4 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2945 and 8167 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(29,6) = HCF(122,29) = HCF(273,122) = HCF(668,273) = HCF(2277,668) = HCF(2945,2277) = HCF(8167,2945) .

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

Step 1: Since 20353 > 1, we apply the division lemma to 20353 and 1, to get

20353 = 1 x 20353 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 20353 is 1

Notice that 1 = HCF(20353,1) .

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Frequently Asked Questions on HCF of 2945, 8167, 20353 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 2945, 8167, 20353?

Answer: HCF of 2945, 8167, 20353 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2945, 8167, 20353 using Euclid's Algorithm?

Answer: For arbitrary numbers 2945, 8167, 20353 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.