Highest Common Factor of 512, 2256 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 512, 2256 i.e. 16 the largest integer that leaves a remainder zero for all numbers.
HCF of 512, 2256 is 16 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 512, 2256 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 512, 2256 is 16.
HCF(512, 2256) = 16
HCF of 512, 2256 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 512, 2256 is 16.
Highest Common Factor of 512,2256 is 16
Step 1: Since 2256 > 512, we apply the division lemma to 2256 and 512, to get
2256 = 512 x 4 + 208
Step 2: Since the reminder 512 ≠ 0, we apply division lemma to 208 and 512, to get
512 = 208 x 2 + 96
Step 3: We consider the new divisor 208 and the new remainder 96, and apply the division lemma to get
208 = 96 x 2 + 16
We consider the new divisor 96 and the new remainder 16, and apply the division lemma to get
96 = 16 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 512 and 2256 is 16
Notice that 16 = HCF(96,16) = HCF(208,96) = HCF(512,208) = HCF(2256,512) .
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Frequently Asked Questions on HCF of 512, 2256 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 512, 2256?
Answer: HCF of 512, 2256 is 16 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 512, 2256 using Euclid's Algorithm?
Answer: For arbitrary numbers 512, 2256 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.