Highest Common Factor of 306, 434, 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 306, 434, 196 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 306, 434, 196 is 2 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 306, 434, 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 306, 434, 196 is 2.
HCF(306, 434, 196) = 2
HCF of 306, 434, 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 306, 434, 196 is 2.
Highest Common Factor of 306,434,196 is 2
Step 1: Since 434 > 306, we apply the division lemma to 434 and 306, to get
434 = 306 x 1 + 128
Step 2: Since the reminder 306 ≠ 0, we apply division lemma to 128 and 306, to get
306 = 128 x 2 + 50
Step 3: We consider the new divisor 128 and the new remainder 50, and apply the division lemma to get
128 = 50 x 2 + 28
We consider the new divisor 50 and the new remainder 28,and apply the division lemma to get
50 = 28 x 1 + 22
We consider the new divisor 28 and the new remainder 22,and apply the division lemma to get
28 = 22 x 1 + 6
We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get
22 = 6 x 3 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 306 and 434 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(28,22) = HCF(50,28) = HCF(128,50) = HCF(306,128) = HCF(434,306) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 196 > 2, we apply the division lemma to 196 and 2, to get
196 = 2 x 98 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 196 is 2
Notice that 2 = HCF(196,2) .
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Frequently Asked Questions on HCF of 306, 434, 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 306, 434, 196?
Answer: HCF of 306, 434, 196 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 306, 434, 196 using Euclid's Algorithm?
Answer: For arbitrary numbers 306, 434, 196 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.