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 1146, 3604, 13192 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 1146, 3604, 13192 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 1146, 3604, 13192 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 1146, 3604, 13192 is 2.
HCF(1146, 3604, 13192) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 1146, 3604, 13192 is 2.
Step 1: Since 3604 > 1146, we apply the division lemma to 3604 and 1146, to get
3604 = 1146 x 3 + 166
Step 2: Since the reminder 1146 ≠ 0, we apply division lemma to 166 and 1146, to get
1146 = 166 x 6 + 150
Step 3: We consider the new divisor 166 and the new remainder 150, and apply the division lemma to get
166 = 150 x 1 + 16
We consider the new divisor 150 and the new remainder 16,and apply the division lemma to get
150 = 16 x 9 + 6
We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get
16 = 6 x 2 + 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 1146 and 3604 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(150,16) = HCF(166,150) = HCF(1146,166) = HCF(3604,1146) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 13192 > 2, we apply the division lemma to 13192 and 2, to get
13192 = 2 x 6596 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 13192 is 2
Notice that 2 = HCF(13192,2) .
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 1146, 3604, 13192?
Answer: HCF of 1146, 3604, 13192 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 1146, 3604, 13192 using Euclid's Algorithm?
Answer: For arbitrary numbers 1146, 3604, 13192 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.