Highest Common Factor of 8040, 8509 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 8040, 8509 i.e. 67 the largest integer that leaves a remainder zero for all numbers.
HCF of 8040, 8509 is 67 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 8040, 8509 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 8040, 8509 is 67.
HCF(8040, 8509) = 67
HCF of 8040, 8509 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8040, 8509 is 67.
Highest Common Factor of 8040,8509 is 67
Step 1: Since 8509 > 8040, we apply the division lemma to 8509 and 8040, to get
8509 = 8040 x 1 + 469
Step 2: Since the reminder 8040 ≠ 0, we apply division lemma to 469 and 8040, to get
8040 = 469 x 17 + 67
Step 3: We consider the new divisor 469 and the new remainder 67, and apply the division lemma to get
469 = 67 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 67, the HCF of 8040 and 8509 is 67
Notice that 67 = HCF(469,67) = HCF(8040,469) = HCF(8509,8040) .
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Frequently Asked Questions on HCF of 8040, 8509 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 8040, 8509?
Answer: HCF of 8040, 8509 is 67 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8040, 8509 using Euclid's Algorithm?
Answer: For arbitrary numbers 8040, 8509 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.