Highest Common Factor of 312, 181 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, 181 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 181 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, 181 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, 181 is 1.
HCF(312, 181) = 1
HCF of 312, 181 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, 181 is 1.
Highest Common Factor of 312,181 is 1
Step 1: Since 312 > 181, we apply the division lemma to 312 and 181, to get
312 = 181 x 1 + 131
Step 2: Since the reminder 181 ≠ 0, we apply division lemma to 131 and 181, to get
181 = 131 x 1 + 50
Step 3: We consider the new divisor 131 and the new remainder 50, and apply the division lemma to get
131 = 50 x 2 + 31
We consider the new divisor 50 and the new remainder 31,and apply the division lemma to get
50 = 31 x 1 + 19
We consider the new divisor 31 and the new remainder 19,and apply the division lemma to get
31 = 19 x 1 + 12
We consider the new divisor 19 and the new remainder 12,and apply the division lemma to get
19 = 12 x 1 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 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 312 and 181 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(19,12) = HCF(31,19) = HCF(50,31) = HCF(131,50) = HCF(181,131) = HCF(312,181) .
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Frequently Asked Questions on HCF of 312, 181 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, 181?
Answer: HCF of 312, 181 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 181 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 181 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.