Highest Common Factor of 312, 515, 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 312, 515, 196 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 515, 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 312, 515, 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 312, 515, 196 is 1.
HCF(312, 515, 196) = 1
HCF of 312, 515, 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 312, 515, 196 is 1.
Highest Common Factor of 312,515,196 is 1
Step 1: Since 515 > 312, we apply the division lemma to 515 and 312, to get
515 = 312 x 1 + 203
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 203 and 312, to get
312 = 203 x 1 + 109
Step 3: We consider the new divisor 203 and the new remainder 109, and apply the division lemma to get
203 = 109 x 1 + 94
We consider the new divisor 109 and the new remainder 94,and apply the division lemma to get
109 = 94 x 1 + 15
We consider the new divisor 94 and the new remainder 15,and apply the division lemma to get
94 = 15 x 6 + 4
We consider the new divisor 15 and the new remainder 4,and apply the division lemma to get
15 = 4 x 3 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 312 and 515 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(15,4) = HCF(94,15) = HCF(109,94) = HCF(203,109) = HCF(312,203) = HCF(515,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 196 > 1, we apply the division lemma to 196 and 1, to get
196 = 1 x 196 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 196 is 1
Notice that 1 = HCF(196,1) .
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Frequently Asked Questions on HCF of 312, 515, 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 312, 515, 196?
Answer: HCF of 312, 515, 196 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 515, 196 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 515, 196 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
