Highest Common Factor of 655, 508, 413 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, 508, 413 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 655, 508, 413 is 1 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, 508, 413 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, 508, 413 is 1.
HCF(655, 508, 413) = 1
HCF of 655, 508, 413 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, 508, 413 is 1.
Highest Common Factor of 655,508,413 is 1
Step 1: Since 655 > 508, we apply the division lemma to 655 and 508, to get
655 = 508 x 1 + 147
Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 147 and 508, to get
508 = 147 x 3 + 67
Step 3: We consider the new divisor 147 and the new remainder 67, and apply the division lemma to get
147 = 67 x 2 + 13
We consider the new divisor 67 and the new remainder 13,and apply the division lemma to get
67 = 13 x 5 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 655 and 508 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(67,13) = HCF(147,67) = HCF(508,147) = HCF(655,508) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 413 > 1, we apply the division lemma to 413 and 1, to get
413 = 1 x 413 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 413 is 1
Notice that 1 = HCF(413,1) .
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Frequently Asked Questions on HCF of 655, 508, 413 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, 508, 413?
Answer: HCF of 655, 508, 413 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 655, 508, 413 using Euclid's Algorithm?
Answer: For arbitrary numbers 655, 508, 413 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.