Highest Common Factor of 197, 308 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 197, 308 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 197, 308 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 197, 308 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 197, 308 is 1.
HCF(197, 308) = 1
HCF of 197, 308 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 197, 308 is 1.
Highest Common Factor of 197,308 is 1
Step 1: Since 308 > 197, we apply the division lemma to 308 and 197, to get
308 = 197 x 1 + 111
Step 2: Since the reminder 197 ≠ 0, we apply division lemma to 111 and 197, to get
197 = 111 x 1 + 86
Step 3: We consider the new divisor 111 and the new remainder 86, and apply the division lemma to get
111 = 86 x 1 + 25
We consider the new divisor 86 and the new remainder 25,and apply the division lemma to get
86 = 25 x 3 + 11
We consider the new divisor 25 and the new remainder 11,and apply the division lemma to get
25 = 11 x 2 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 197 and 308 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(25,11) = HCF(86,25) = HCF(111,86) = HCF(197,111) = HCF(308,197) .
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Frequently Asked Questions on HCF of 197, 308 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 197, 308?
Answer: HCF of 197, 308 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 197, 308 using Euclid's Algorithm?
Answer: For arbitrary numbers 197, 308 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.