Highest Common Factor of 815, 8040 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 815, 8040 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 815, 8040 is 5 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 815, 8040 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 815, 8040 is 5.
HCF(815, 8040) = 5
HCF of 815, 8040 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 815, 8040 is 5.
Highest Common Factor of 815,8040 is 5
Step 1: Since 8040 > 815, we apply the division lemma to 8040 and 815, to get
8040 = 815 x 9 + 705
Step 2: Since the reminder 815 ≠ 0, we apply division lemma to 705 and 815, to get
815 = 705 x 1 + 110
Step 3: We consider the new divisor 705 and the new remainder 110, and apply the division lemma to get
705 = 110 x 6 + 45
We consider the new divisor 110 and the new remainder 45,and apply the division lemma to get
110 = 45 x 2 + 20
We consider the new divisor 45 and the new remainder 20,and apply the division lemma to get
45 = 20 x 2 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 815 and 8040 is 5
Notice that 5 = HCF(20,5) = HCF(45,20) = HCF(110,45) = HCF(705,110) = HCF(815,705) = HCF(8040,815) .
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Frequently Asked Questions on HCF of 815, 8040 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 815, 8040?
Answer: HCF of 815, 8040 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 815, 8040 using Euclid's Algorithm?
Answer: For arbitrary numbers 815, 8040 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
