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 313, 745, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 313, 745, 31 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 313, 745, 31 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 313, 745, 31 is 1.
HCF(313, 745, 31) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 313, 745, 31 is 1.
Step 1: Since 745 > 313, we apply the division lemma to 745 and 313, to get
745 = 313 x 2 + 119
Step 2: Since the reminder 313 ≠ 0, we apply division lemma to 119 and 313, to get
313 = 119 x 2 + 75
Step 3: We consider the new divisor 119 and the new remainder 75, and apply the division lemma to get
119 = 75 x 1 + 44
We consider the new divisor 75 and the new remainder 44,and apply the division lemma to get
75 = 44 x 1 + 31
We consider the new divisor 44 and the new remainder 31,and apply the division lemma to get
44 = 31 x 1 + 13
We consider the new divisor 31 and the new remainder 13,and apply the division lemma to get
31 = 13 x 2 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 313 and 745 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(31,13) = HCF(44,31) = HCF(75,44) = HCF(119,75) = HCF(313,119) = HCF(745,313) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 31 > 1, we apply the division lemma to 31 and 1, to get
31 = 1 x 31 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31 is 1
Notice that 1 = HCF(31,1) .
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 313, 745, 31?
Answer: HCF of 313, 745, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 313, 745, 31 using Euclid's Algorithm?
Answer: For arbitrary numbers 313, 745, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.