Highest Common Factor of 2945, 8635 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, 8635 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 2945, 8635 is 5 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, 8635 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, 8635 is 5.
HCF(2945, 8635) = 5
HCF of 2945, 8635 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2945, 8635 is 5.
Highest Common Factor of 2945,8635 is 5
Step 1: Since 8635 > 2945, we apply the division lemma to 8635 and 2945, to get
8635 = 2945 x 2 + 2745
Step 2: Since the reminder 2945 ≠ 0, we apply division lemma to 2745 and 2945, to get
2945 = 2745 x 1 + 200
Step 3: We consider the new divisor 2745 and the new remainder 200, and apply the division lemma to get
2745 = 200 x 13 + 145
We consider the new divisor 200 and the new remainder 145,and apply the division lemma to get
200 = 145 x 1 + 55
We consider the new divisor 145 and the new remainder 55,and apply the division lemma to get
145 = 55 x 2 + 35
We consider the new divisor 55 and the new remainder 35,and apply the division lemma to get
55 = 35 x 1 + 20
We consider the new divisor 35 and the new remainder 20,and apply the division lemma to get
35 = 20 x 1 + 15
We consider the new divisor 20 and the new remainder 15,and apply the division lemma to get
20 = 15 x 1 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 2945 and 8635 is 5
Notice that 5 = HCF(15,5) = HCF(20,15) = HCF(35,20) = HCF(55,35) = HCF(145,55) = HCF(200,145) = HCF(2745,200) = HCF(2945,2745) = HCF(8635,2945) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2945, 8635 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, 8635?
Answer: HCF of 2945, 8635 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2945, 8635 using Euclid's Algorithm?
Answer: For arbitrary numbers 2945, 8635 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.