Highest Common Factor of 6574, 5005 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 6574, 5005 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6574, 5005 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 6574, 5005 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 6574, 5005 is 1.
HCF(6574, 5005) = 1
HCF of 6574, 5005 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6574, 5005 is 1.
Highest Common Factor of 6574,5005 is 1
Step 1: Since 6574 > 5005, we apply the division lemma to 6574 and 5005, to get
6574 = 5005 x 1 + 1569
Step 2: Since the reminder 5005 ≠ 0, we apply division lemma to 1569 and 5005, to get
5005 = 1569 x 3 + 298
Step 3: We consider the new divisor 1569 and the new remainder 298, and apply the division lemma to get
1569 = 298 x 5 + 79
We consider the new divisor 298 and the new remainder 79,and apply the division lemma to get
298 = 79 x 3 + 61
We consider the new divisor 79 and the new remainder 61,and apply the division lemma to get
79 = 61 x 1 + 18
We consider the new divisor 61 and the new remainder 18,and apply the division lemma to get
61 = 18 x 3 + 7
We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get
18 = 7 x 2 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6574 and 5005 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(61,18) = HCF(79,61) = HCF(298,79) = HCF(1569,298) = HCF(5005,1569) = HCF(6574,5005) .
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Frequently Asked Questions on HCF of 6574, 5005 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 6574, 5005?
Answer: HCF of 6574, 5005 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6574, 5005 using Euclid's Algorithm?
Answer: For arbitrary numbers 6574, 5005 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.