Highest Common Factor of 655, 825 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, 825 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 655, 825 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, 825 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, 825 is 5.
HCF(655, 825) = 5
HCF of 655, 825 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, 825 is 5.
Highest Common Factor of 655,825 is 5
Step 1: Since 825 > 655, we apply the division lemma to 825 and 655, to get
825 = 655 x 1 + 170
Step 2: Since the reminder 655 ≠ 0, we apply division lemma to 170 and 655, to get
655 = 170 x 3 + 145
Step 3: We consider the new divisor 170 and the new remainder 145, and apply the division lemma to get
170 = 145 x 1 + 25
We consider the new divisor 145 and the new remainder 25,and apply the division lemma to get
145 = 25 x 5 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 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 655 and 825 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(145,25) = HCF(170,145) = HCF(655,170) = HCF(825,655) .
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Frequently Asked Questions on HCF of 655, 825 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, 825?
Answer: HCF of 655, 825 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 655, 825 using Euclid's Algorithm?
Answer: For arbitrary numbers 655, 825 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.