Highest Common Factor of 7055, 9665 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 7055, 9665 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 7055, 9665 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 7055, 9665 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 7055, 9665 is 5.
HCF(7055, 9665) = 5
HCF of 7055, 9665 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7055, 9665 is 5.
Highest Common Factor of 7055,9665 is 5
Step 1: Since 9665 > 7055, we apply the division lemma to 9665 and 7055, to get
9665 = 7055 x 1 + 2610
Step 2: Since the reminder 7055 ≠ 0, we apply division lemma to 2610 and 7055, to get
7055 = 2610 x 2 + 1835
Step 3: We consider the new divisor 2610 and the new remainder 1835, and apply the division lemma to get
2610 = 1835 x 1 + 775
We consider the new divisor 1835 and the new remainder 775,and apply the division lemma to get
1835 = 775 x 2 + 285
We consider the new divisor 775 and the new remainder 285,and apply the division lemma to get
775 = 285 x 2 + 205
We consider the new divisor 285 and the new remainder 205,and apply the division lemma to get
285 = 205 x 1 + 80
We consider the new divisor 205 and the new remainder 80,and apply the division lemma to get
205 = 80 x 2 + 45
We consider the new divisor 80 and the new remainder 45,and apply the division lemma to get
80 = 45 x 1 + 35
We consider the new divisor 45 and the new remainder 35,and apply the division lemma to get
45 = 35 x 1 + 10
We consider the new divisor 35 and the new remainder 10,and apply the division lemma to get
35 = 10 x 3 + 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 7055 and 9665 is 5
Notice that 5 = HCF(10,5) = HCF(35,10) = HCF(45,35) = HCF(80,45) = HCF(205,80) = HCF(285,205) = HCF(775,285) = HCF(1835,775) = HCF(2610,1835) = HCF(7055,2610) = HCF(9665,7055) .
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Frequently Asked Questions on HCF of 7055, 9665 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 7055, 9665?
Answer: HCF of 7055, 9665 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7055, 9665 using Euclid's Algorithm?
Answer: For arbitrary numbers 7055, 9665 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.