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 993, 104, 613 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 993, 104, 613 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 993, 104, 613 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 993, 104, 613 is 1.
HCF(993, 104, 613) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 993, 104, 613 is 1.
Step 1: Since 993 > 104, we apply the division lemma to 993 and 104, to get
993 = 104 x 9 + 57
Step 2: Since the reminder 104 ≠ 0, we apply division lemma to 57 and 104, to get
104 = 57 x 1 + 47
Step 3: We consider the new divisor 57 and the new remainder 47, and apply the division lemma to get
57 = 47 x 1 + 10
We consider the new divisor 47 and the new remainder 10,and apply the division lemma to get
47 = 10 x 4 + 7
We consider the new divisor 10 and the new remainder 7,and apply the division lemma to get
10 = 7 x 1 + 3
We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get
7 = 3 x 2 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 993 and 104 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(10,7) = HCF(47,10) = HCF(57,47) = HCF(104,57) = HCF(993,104) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 613 > 1, we apply the division lemma to 613 and 1, to get
613 = 1 x 613 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 613 is 1
Notice that 1 = HCF(613,1) .
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 993, 104, 613?
Answer: HCF of 993, 104, 613 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 993, 104, 613 using Euclid's Algorithm?
Answer: For arbitrary numbers 993, 104, 613 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.