Highest Common Factor of 576, 2226 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 576, 2226 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 576, 2226 is 6 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 576, 2226 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 576, 2226 is 6.
HCF(576, 2226) = 6
HCF of 576, 2226 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 576, 2226 is 6.
Highest Common Factor of 576,2226 is 6
Step 1: Since 2226 > 576, we apply the division lemma to 2226 and 576, to get
2226 = 576 x 3 + 498
Step 2: Since the reminder 576 ≠ 0, we apply division lemma to 498 and 576, to get
576 = 498 x 1 + 78
Step 3: We consider the new divisor 498 and the new remainder 78, and apply the division lemma to get
498 = 78 x 6 + 30
We consider the new divisor 78 and the new remainder 30,and apply the division lemma to get
78 = 30 x 2 + 18
We consider the new divisor 30 and the new remainder 18,and apply the division lemma to get
30 = 18 x 1 + 12
We consider the new divisor 18 and the new remainder 12,and apply the division lemma to get
18 = 12 x 1 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 576 and 2226 is 6
Notice that 6 = HCF(12,6) = HCF(18,12) = HCF(30,18) = HCF(78,30) = HCF(498,78) = HCF(576,498) = HCF(2226,576) .
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Frequently Asked Questions on HCF of 576, 2226 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 576, 2226?
Answer: HCF of 576, 2226 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 576, 2226 using Euclid's Algorithm?
Answer: For arbitrary numbers 576, 2226 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.