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 315, 514 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 315, 514 is 1 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 315, 514 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 315, 514 is 1.
HCF(315, 514) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 315, 514 is 1.
Step 1: Since 514 > 315, we apply the division lemma to 514 and 315, to get
514 = 315 x 1 + 199
Step 2: Since the reminder 315 ≠ 0, we apply division lemma to 199 and 315, to get
315 = 199 x 1 + 116
Step 3: We consider the new divisor 199 and the new remainder 116, and apply the division lemma to get
199 = 116 x 1 + 83
We consider the new divisor 116 and the new remainder 83,and apply the division lemma to get
116 = 83 x 1 + 33
We consider the new divisor 83 and the new remainder 33,and apply the division lemma to get
83 = 33 x 2 + 17
We consider the new divisor 33 and the new remainder 17,and apply the division lemma to get
33 = 17 x 1 + 16
We consider the new divisor 17 and the new remainder 16,and apply the division lemma to get
17 = 16 x 1 + 1
We consider the new divisor 16 and the new remainder 1,and apply the division lemma to get
16 = 1 x 16 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 315 and 514 is 1
Notice that 1 = HCF(16,1) = HCF(17,16) = HCF(33,17) = HCF(83,33) = HCF(116,83) = HCF(199,116) = HCF(315,199) = HCF(514,315) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 315, 514?
Answer: HCF of 315, 514 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 315, 514 using Euclid's Algorithm?
Answer: For arbitrary numbers 315, 514 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.