Highest Common Factor of 2120, 8233 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 2120, 8233 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2120, 8233 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 2120, 8233 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 2120, 8233 is 1.
HCF(2120, 8233) = 1
HCF of 2120, 8233 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2120, 8233 is 1.
Highest Common Factor of 2120,8233 is 1
Step 1: Since 8233 > 2120, we apply the division lemma to 8233 and 2120, to get
8233 = 2120 x 3 + 1873
Step 2: Since the reminder 2120 ≠ 0, we apply division lemma to 1873 and 2120, to get
2120 = 1873 x 1 + 247
Step 3: We consider the new divisor 1873 and the new remainder 247, and apply the division lemma to get
1873 = 247 x 7 + 144
We consider the new divisor 247 and the new remainder 144,and apply the division lemma to get
247 = 144 x 1 + 103
We consider the new divisor 144 and the new remainder 103,and apply the division lemma to get
144 = 103 x 1 + 41
We consider the new divisor 103 and the new remainder 41,and apply the division lemma to get
103 = 41 x 2 + 21
We consider the new divisor 41 and the new remainder 21,and apply the division lemma to get
41 = 21 x 1 + 20
We consider the new divisor 21 and the new remainder 20,and apply the division lemma to get
21 = 20 x 1 + 1
We consider the new divisor 20 and the new remainder 1,and apply the division lemma to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2120 and 8233 is 1
Notice that 1 = HCF(20,1) = HCF(21,20) = HCF(41,21) = HCF(103,41) = HCF(144,103) = HCF(247,144) = HCF(1873,247) = HCF(2120,1873) = HCF(8233,2120) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2120, 8233 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 2120, 8233?
Answer: HCF of 2120, 8233 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2120, 8233 using Euclid's Algorithm?
Answer: For arbitrary numbers 2120, 8233 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.