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 808, 310, 296 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 808, 310, 296 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 808, 310, 296 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 808, 310, 296 is 2.
HCF(808, 310, 296) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 808, 310, 296 is 2.
Step 1: Since 808 > 310, we apply the division lemma to 808 and 310, to get
808 = 310 x 2 + 188
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 188 and 310, to get
310 = 188 x 1 + 122
Step 3: We consider the new divisor 188 and the new remainder 122, and apply the division lemma to get
188 = 122 x 1 + 66
We consider the new divisor 122 and the new remainder 66,and apply the division lemma to get
122 = 66 x 1 + 56
We consider the new divisor 66 and the new remainder 56,and apply the division lemma to get
66 = 56 x 1 + 10
We consider the new divisor 56 and the new remainder 10,and apply the division lemma to get
56 = 10 x 5 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma 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 808 and 310 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(56,10) = HCF(66,56) = HCF(122,66) = HCF(188,122) = HCF(310,188) = HCF(808,310) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 296 > 2, we apply the division lemma to 296 and 2, to get
296 = 2 x 148 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 296 is 2
Notice that 2 = HCF(296,2) .
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 808, 310, 296?
Answer: HCF of 808, 310, 296 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 808, 310, 296 using Euclid's Algorithm?
Answer: For arbitrary numbers 808, 310, 296 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.