Highest Common Factor of 432, 314 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 432, 314 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 432, 314 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 432, 314 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 432, 314 is 2.
HCF(432, 314) = 2
HCF of 432, 314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 432, 314 is 2.
Highest Common Factor of 432,314 is 2
Step 1: Since 432 > 314, we apply the division lemma to 432 and 314, to get
432 = 314 x 1 + 118
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 118 and 314, to get
314 = 118 x 2 + 78
Step 3: We consider the new divisor 118 and the new remainder 78, and apply the division lemma to get
118 = 78 x 1 + 40
We consider the new divisor 78 and the new remainder 40,and apply the division lemma to get
78 = 40 x 1 + 38
We consider the new divisor 40 and the new remainder 38,and apply the division lemma to get
40 = 38 x 1 + 2
We consider the new divisor 38 and the new remainder 2,and apply the division lemma to get
38 = 2 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 432 and 314 is 2
Notice that 2 = HCF(38,2) = HCF(40,38) = HCF(78,40) = HCF(118,78) = HCF(314,118) = HCF(432,314) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 432, 314 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 432, 314?
Answer: HCF of 432, 314 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 432, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 432, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.