Highest Common Factor of 256, 2103 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 256, 2103 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 256, 2103 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 256, 2103 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 256, 2103 is 1.
HCF(256, 2103) = 1
HCF of 256, 2103 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 256, 2103 is 1.
Highest Common Factor of 256,2103 is 1
Step 1: Since 2103 > 256, we apply the division lemma to 2103 and 256, to get
2103 = 256 x 8 + 55
Step 2: Since the reminder 256 ≠ 0, we apply division lemma to 55 and 256, to get
256 = 55 x 4 + 36
Step 3: We consider the new divisor 55 and the new remainder 36, and apply the division lemma to get
55 = 36 x 1 + 19
We consider the new divisor 36 and the new remainder 19,and apply the division lemma to get
36 = 19 x 1 + 17
We consider the new divisor 19 and the new remainder 17,and apply the division lemma to get
19 = 17 x 1 + 2
We consider the new divisor 17 and the new remainder 2,and apply the division lemma to get
17 = 2 x 8 + 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 256 and 2103 is 1
Notice that 1 = HCF(2,1) = HCF(17,2) = HCF(19,17) = HCF(36,19) = HCF(55,36) = HCF(256,55) = HCF(2103,256) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 256, 2103 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 256, 2103?
Answer: HCF of 256, 2103 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 256, 2103 using Euclid's Algorithm?
Answer: For arbitrary numbers 256, 2103 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.