Highest Common Factor of 312, 458, 380 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, 458, 380 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 458, 380 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 312, 458, 380 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, 458, 380 is 2.
HCF(312, 458, 380) = 2
HCF of 312, 458, 380 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, 458, 380 is 2.
Highest Common Factor of 312,458,380 is 2
Step 1: Since 458 > 312, we apply the division lemma to 458 and 312, to get
458 = 312 x 1 + 146
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 146 and 312, to get
312 = 146 x 2 + 20
Step 3: We consider the new divisor 146 and the new remainder 20, and apply the division lemma to get
146 = 20 x 7 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 312 and 458 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(146,20) = HCF(312,146) = HCF(458,312) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 380 > 2, we apply the division lemma to 380 and 2, to get
380 = 2 x 190 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 380 is 2
Notice that 2 = HCF(380,2) .
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Frequently Asked Questions on HCF of 312, 458, 380 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, 458, 380?
Answer: HCF of 312, 458, 380 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 458, 380 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 458, 380 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.