Highest Common Factor of 8578, 8005 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 8578, 8005 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8578, 8005 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 8578, 8005 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 8578, 8005 is 1.
HCF(8578, 8005) = 1
HCF of 8578, 8005 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8578, 8005 is 1.
Highest Common Factor of 8578,8005 is 1
Step 1: Since 8578 > 8005, we apply the division lemma to 8578 and 8005, to get
8578 = 8005 x 1 + 573
Step 2: Since the reminder 8005 ≠ 0, we apply division lemma to 573 and 8005, to get
8005 = 573 x 13 + 556
Step 3: We consider the new divisor 573 and the new remainder 556, and apply the division lemma to get
573 = 556 x 1 + 17
We consider the new divisor 556 and the new remainder 17,and apply the division lemma to get
556 = 17 x 32 + 12
We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get
17 = 12 x 1 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 8578 and 8005 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(556,17) = HCF(573,556) = HCF(8005,573) = HCF(8578,8005) .
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Frequently Asked Questions on HCF of 8578, 8005 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 8578, 8005?
Answer: HCF of 8578, 8005 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8578, 8005 using Euclid's Algorithm?
Answer: For arbitrary numbers 8578, 8005 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.