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 310, 32814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 32814 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 310, 32814 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 310, 32814 is 2.
HCF(310, 32814) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 310, 32814 is 2.
Step 1: Since 32814 > 310, we apply the division lemma to 32814 and 310, to get
32814 = 310 x 105 + 264
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 264 and 310, to get
310 = 264 x 1 + 46
Step 3: We consider the new divisor 264 and the new remainder 46, and apply the division lemma to get
264 = 46 x 5 + 34
We consider the new divisor 46 and the new remainder 34,and apply the division lemma to get
46 = 34 x 1 + 12
We consider the new divisor 34 and the new remainder 12,and apply the division lemma to get
34 = 12 x 2 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 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 310 and 32814 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(34,12) = HCF(46,34) = HCF(264,46) = HCF(310,264) = HCF(32814,310) .
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 310, 32814?
Answer: HCF of 310, 32814 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 32814 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 32814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.