Highest Common Factor of 668, 384, 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 668, 384, 314 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 668, 384, 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 668, 384, 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 668, 384, 314 is 2.
HCF(668, 384, 314) = 2
HCF of 668, 384, 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 668, 384, 314 is 2.
Highest Common Factor of 668,384,314 is 2
Step 1: Since 668 > 384, we apply the division lemma to 668 and 384, to get
668 = 384 x 1 + 284
Step 2: Since the reminder 384 ≠ 0, we apply division lemma to 284 and 384, to get
384 = 284 x 1 + 100
Step 3: We consider the new divisor 284 and the new remainder 100, and apply the division lemma to get
284 = 100 x 2 + 84
We consider the new divisor 100 and the new remainder 84,and apply the division lemma to get
100 = 84 x 1 + 16
We consider the new divisor 84 and the new remainder 16,and apply the division lemma to get
84 = 16 x 5 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 668 and 384 is 4
Notice that 4 = HCF(16,4) = HCF(84,16) = HCF(100,84) = HCF(284,100) = HCF(384,284) = HCF(668,384) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 314 > 4, we apply the division lemma to 314 and 4, to get
314 = 4 x 78 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 314 is 2
Notice that 2 = HCF(4,2) = HCF(314,4) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 668, 384, 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 668, 384, 314?
Answer: HCF of 668, 384, 314 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 668, 384, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 668, 384, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.