Highest Common Factor of 576, 69567 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, 69567 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 576, 69567 is 3 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, 69567 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, 69567 is 3.
HCF(576, 69567) = 3
HCF of 576, 69567 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, 69567 is 3.
Highest Common Factor of 576,69567 is 3
Step 1: Since 69567 > 576, we apply the division lemma to 69567 and 576, to get
69567 = 576 x 120 + 447
Step 2: Since the reminder 576 ≠ 0, we apply division lemma to 447 and 576, to get
576 = 447 x 1 + 129
Step 3: We consider the new divisor 447 and the new remainder 129, and apply the division lemma to get
447 = 129 x 3 + 60
We consider the new divisor 129 and the new remainder 60,and apply the division lemma to get
129 = 60 x 2 + 9
We consider the new divisor 60 and the new remainder 9,and apply the division lemma to get
60 = 9 x 6 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 576 and 69567 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(60,9) = HCF(129,60) = HCF(447,129) = HCF(576,447) = HCF(69567,576) .
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Frequently Asked Questions on HCF of 576, 69567 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, 69567?
Answer: HCF of 576, 69567 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 576, 69567 using Euclid's Algorithm?
Answer: For arbitrary numbers 576, 69567 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.