Highest Common Factor of 655, 6695 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 655, 6695 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 655, 6695 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 655, 6695 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 655, 6695 is 5.
HCF(655, 6695) = 5
HCF of 655, 6695 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 655, 6695 is 5.
Highest Common Factor of 655,6695 is 5
Step 1: Since 6695 > 655, we apply the division lemma to 6695 and 655, to get
6695 = 655 x 10 + 145
Step 2: Since the reminder 655 ≠ 0, we apply division lemma to 145 and 655, to get
655 = 145 x 4 + 75
Step 3: We consider the new divisor 145 and the new remainder 75, and apply the division lemma to get
145 = 75 x 1 + 70
We consider the new divisor 75 and the new remainder 70,and apply the division lemma to get
75 = 70 x 1 + 5
We consider the new divisor 70 and the new remainder 5,and apply the division lemma to get
70 = 5 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 655 and 6695 is 5
Notice that 5 = HCF(70,5) = HCF(75,70) = HCF(145,75) = HCF(655,145) = HCF(6695,655) .
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Frequently Asked Questions on HCF of 655, 6695 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 655, 6695?
Answer: HCF of 655, 6695 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 655, 6695 using Euclid's Algorithm?
Answer: For arbitrary numbers 655, 6695 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.