Highest Common Factor of 202, 8500, 3052 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 202, 8500, 3052 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 202, 8500, 3052 is 2 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 202, 8500, 3052 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 202, 8500, 3052 is 2.
HCF(202, 8500, 3052) = 2
HCF of 202, 8500, 3052 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 202, 8500, 3052 is 2.
Highest Common Factor of 202,8500,3052 is 2
Step 1: Since 8500 > 202, we apply the division lemma to 8500 and 202, to get
8500 = 202 x 42 + 16
Step 2: Since the reminder 202 ≠ 0, we apply division lemma to 16 and 202, to get
202 = 16 x 12 + 10
Step 3: We consider the new divisor 16 and the new remainder 10, and apply the division lemma to get
16 = 10 x 1 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 202 and 8500 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(202,16) = HCF(8500,202) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3052 > 2, we apply the division lemma to 3052 and 2, to get
3052 = 2 x 1526 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 3052 is 2
Notice that 2 = HCF(3052,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 202, 8500, 3052 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 202, 8500, 3052?
Answer: HCF of 202, 8500, 3052 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 202, 8500, 3052 using Euclid's Algorithm?
Answer: For arbitrary numbers 202, 8500, 3052 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.