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 675, 12327 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 675, 12327 is 3 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 675, 12327 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 675, 12327 is 3.
HCF(675, 12327) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 675, 12327 is 3.
Step 1: Since 12327 > 675, we apply the division lemma to 12327 and 675, to get
12327 = 675 x 18 + 177
Step 2: Since the reminder 675 ≠ 0, we apply division lemma to 177 and 675, to get
675 = 177 x 3 + 144
Step 3: We consider the new divisor 177 and the new remainder 144, and apply the division lemma to get
177 = 144 x 1 + 33
We consider the new divisor 144 and the new remainder 33,and apply the division lemma to get
144 = 33 x 4 + 12
We consider the new divisor 33 and the new remainder 12,and apply the division lemma to get
33 = 12 x 2 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 675 and 12327 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(33,12) = HCF(144,33) = HCF(177,144) = HCF(675,177) = HCF(12327,675) .
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 675, 12327?
Answer: HCF of 675, 12327 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 675, 12327 using Euclid's Algorithm?
Answer: For arbitrary numbers 675, 12327 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.