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 4108, 4123, 12652 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 4108, 4123, 12652 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 4108, 4123, 12652 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 4108, 4123, 12652 is 1.
HCF(4108, 4123, 12652) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 4108, 4123, 12652 is 1.
Step 1: Since 4123 > 4108, we apply the division lemma to 4123 and 4108, to get
4123 = 4108 x 1 + 15
Step 2: Since the reminder 4108 ≠ 0, we apply division lemma to 15 and 4108, to get
4108 = 15 x 273 + 13
Step 3: We consider the new divisor 15 and the new remainder 13, and apply the division lemma to get
15 = 13 x 1 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 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 4108 and 4123 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(4108,15) = HCF(4123,4108) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 12652 > 1, we apply the division lemma to 12652 and 1, to get
12652 = 1 x 12652 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 12652 is 1
Notice that 1 = HCF(12652,1) .
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 4108, 4123, 12652?
Answer: HCF of 4108, 4123, 12652 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 4108, 4123, 12652 using Euclid's Algorithm?
Answer: For arbitrary numbers 4108, 4123, 12652 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.