Highest Common Factor of 8576, 1569 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 8576, 1569 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8576, 1569 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 8576, 1569 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 8576, 1569 is 1.
HCF(8576, 1569) = 1
HCF of 8576, 1569 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8576, 1569 is 1.
Highest Common Factor of 8576,1569 is 1
Step 1: Since 8576 > 1569, we apply the division lemma to 8576 and 1569, to get
8576 = 1569 x 5 + 731
Step 2: Since the reminder 1569 ≠ 0, we apply division lemma to 731 and 1569, to get
1569 = 731 x 2 + 107
Step 3: We consider the new divisor 731 and the new remainder 107, and apply the division lemma to get
731 = 107 x 6 + 89
We consider the new divisor 107 and the new remainder 89,and apply the division lemma to get
107 = 89 x 1 + 18
We consider the new divisor 89 and the new remainder 18,and apply the division lemma to get
89 = 18 x 4 + 17
We consider the new divisor 18 and the new remainder 17,and apply the division lemma to get
18 = 17 x 1 + 1
We consider the new divisor 17 and the new remainder 1,and apply the division lemma to get
17 = 1 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8576 and 1569 is 1
Notice that 1 = HCF(17,1) = HCF(18,17) = HCF(89,18) = HCF(107,89) = HCF(731,107) = HCF(1569,731) = HCF(8576,1569) .
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Frequently Asked Questions on HCF of 8576, 1569 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 8576, 1569?
Answer: HCF of 8576, 1569 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8576, 1569 using Euclid's Algorithm?
Answer: For arbitrary numbers 8576, 1569 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.