Highest Common Factor of 7705, 8115 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 7705, 8115 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 7705, 8115 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 7705, 8115 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 7705, 8115 is 5.
HCF(7705, 8115) = 5
HCF of 7705, 8115 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7705, 8115 is 5.
Highest Common Factor of 7705,8115 is 5
Step 1: Since 8115 > 7705, we apply the division lemma to 8115 and 7705, to get
8115 = 7705 x 1 + 410
Step 2: Since the reminder 7705 ≠ 0, we apply division lemma to 410 and 7705, to get
7705 = 410 x 18 + 325
Step 3: We consider the new divisor 410 and the new remainder 325, and apply the division lemma to get
410 = 325 x 1 + 85
We consider the new divisor 325 and the new remainder 85,and apply the division lemma to get
325 = 85 x 3 + 70
We consider the new divisor 85 and the new remainder 70,and apply the division lemma to get
85 = 70 x 1 + 15
We consider the new divisor 70 and the new remainder 15,and apply the division lemma to get
70 = 15 x 4 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 7705 and 8115 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(70,15) = HCF(85,70) = HCF(325,85) = HCF(410,325) = HCF(7705,410) = HCF(8115,7705) .
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Frequently Asked Questions on HCF of 7705, 8115 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 7705, 8115?
Answer: HCF of 7705, 8115 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7705, 8115 using Euclid's Algorithm?
Answer: For arbitrary numbers 7705, 8115 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.