Highest Common Factor of 513, 196 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 513, 196 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 513, 196 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 513, 196 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 513, 196 is 1.
HCF(513, 196) = 1
HCF of 513, 196 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 513, 196 is 1.
Highest Common Factor of 513,196 is 1
Step 1: Since 513 > 196, we apply the division lemma to 513 and 196, to get
513 = 196 x 2 + 121
Step 2: Since the reminder 196 ≠ 0, we apply division lemma to 121 and 196, to get
196 = 121 x 1 + 75
Step 3: We consider the new divisor 121 and the new remainder 75, and apply the division lemma to get
121 = 75 x 1 + 46
We consider the new divisor 75 and the new remainder 46,and apply the division lemma to get
75 = 46 x 1 + 29
We consider the new divisor 46 and the new remainder 29,and apply the division lemma to get
46 = 29 x 1 + 17
We consider the new divisor 29 and the new remainder 17,and apply the division lemma to get
29 = 17 x 1 + 12
We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get
17 = 12 x 1 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 513 and 196 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(29,17) = HCF(46,29) = HCF(75,46) = HCF(121,75) = HCF(196,121) = HCF(513,196) .
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Frequently Asked Questions on HCF of 513, 196 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 513, 196?
Answer: HCF of 513, 196 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 513, 196 using Euclid's Algorithm?
Answer: For arbitrary numbers 513, 196 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
