Highest Common Factor of 510, 450, 312 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 510, 450, 312 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 510, 450, 312 is 6 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 510, 450, 312 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 510, 450, 312 is 6.
HCF(510, 450, 312) = 6
HCF of 510, 450, 312 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 510, 450, 312 is 6.
Highest Common Factor of 510,450,312 is 6
Step 1: Since 510 > 450, we apply the division lemma to 510 and 450, to get
510 = 450 x 1 + 60
Step 2: Since the reminder 450 ≠ 0, we apply division lemma to 60 and 450, to get
450 = 60 x 7 + 30
Step 3: We consider the new divisor 60 and the new remainder 30, and apply the division lemma to get
60 = 30 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 510 and 450 is 30
Notice that 30 = HCF(60,30) = HCF(450,60) = HCF(510,450) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 312 > 30, we apply the division lemma to 312 and 30, to get
312 = 30 x 10 + 12
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 12 and 30, to get
30 = 12 x 2 + 6
Step 3: We consider the new divisor 12 and the new remainder 6, and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 30 and 312 is 6
Notice that 6 = HCF(12,6) = HCF(30,12) = HCF(312,30) .
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Frequently Asked Questions on HCF of 510, 450, 312 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 510, 450, 312?
Answer: HCF of 510, 450, 312 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 510, 450, 312 using Euclid's Algorithm?
Answer: For arbitrary numbers 510, 450, 312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.