Highest Common Factor of 314, 812, 150 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 314, 812, 150 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 314, 812, 150 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 314, 812, 150 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 314, 812, 150 is 2.
HCF(314, 812, 150) = 2
HCF of 314, 812, 150 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 314, 812, 150 is 2.
Highest Common Factor of 314,812,150 is 2
Step 1: Since 812 > 314, we apply the division lemma to 812 and 314, to get
812 = 314 x 2 + 184
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 184 and 314, to get
314 = 184 x 1 + 130
Step 3: We consider the new divisor 184 and the new remainder 130, and apply the division lemma to get
184 = 130 x 1 + 54
We consider the new divisor 130 and the new remainder 54,and apply the division lemma to get
130 = 54 x 2 + 22
We consider the new divisor 54 and the new remainder 22,and apply the division lemma to get
54 = 22 x 2 + 10
We consider the new divisor 22 and the new remainder 10,and apply the division lemma to get
22 = 10 x 2 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 314 and 812 is 2
Notice that 2 = HCF(10,2) = HCF(22,10) = HCF(54,22) = HCF(130,54) = HCF(184,130) = HCF(314,184) = HCF(812,314) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 150 > 2, we apply the division lemma to 150 and 2, to get
150 = 2 x 75 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 150 is 2
Notice that 2 = HCF(150,2) .
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Frequently Asked Questions on HCF of 314, 812, 150 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 314, 812, 150?
Answer: HCF of 314, 812, 150 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 314, 812, 150 using Euclid's Algorithm?
Answer: For arbitrary numbers 314, 812, 150 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
