Highest Common Factor of 312, 186, 273 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, 186, 273 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 186, 273 is 3 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, 186, 273 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, 186, 273 is 3.
HCF(312, 186, 273) = 3
HCF of 312, 186, 273 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, 186, 273 is 3.
Highest Common Factor of 312,186,273 is 3
Step 1: Since 312 > 186, we apply the division lemma to 312 and 186, to get
312 = 186 x 1 + 126
Step 2: Since the reminder 186 ≠ 0, we apply division lemma to 126 and 186, to get
186 = 126 x 1 + 60
Step 3: We consider the new divisor 126 and the new remainder 60, and apply the division lemma to get
126 = 60 x 2 + 6
We consider the new divisor 60 and the new remainder 6, and apply the division lemma to get
60 = 6 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 312 and 186 is 6
Notice that 6 = HCF(60,6) = HCF(126,60) = HCF(186,126) = HCF(312,186) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 273 > 6, we apply the division lemma to 273 and 6, to get
273 = 6 x 45 + 3
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 3 and 6, to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 6 and 273 is 3
Notice that 3 = HCF(6,3) = HCF(273,6) .
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Frequently Asked Questions on HCF of 312, 186, 273 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, 186, 273?
Answer: HCF of 312, 186, 273 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 186, 273 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 186, 273 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.