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 132, 612, 285 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 132, 612, 285 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 132, 612, 285 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 132, 612, 285 is 3.
HCF(132, 612, 285) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 132, 612, 285 is 3.
Step 1: Since 612 > 132, we apply the division lemma to 612 and 132, to get
612 = 132 x 4 + 84
Step 2: Since the reminder 132 ≠ 0, we apply division lemma to 84 and 132, to get
132 = 84 x 1 + 48
Step 3: We consider the new divisor 84 and the new remainder 48, and apply the division lemma to get
84 = 48 x 1 + 36
We consider the new divisor 48 and the new remainder 36,and apply the division lemma to get
48 = 36 x 1 + 12
We consider the new divisor 36 and the new remainder 12,and apply the division lemma to get
36 = 12 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 132 and 612 is 12
Notice that 12 = HCF(36,12) = HCF(48,36) = HCF(84,48) = HCF(132,84) = HCF(612,132) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 285 > 12, we apply the division lemma to 285 and 12, to get
285 = 12 x 23 + 9
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 9 and 12, to get
12 = 9 x 1 + 3
Step 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 12 and 285 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(285,12) .
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 132, 612, 285?
Answer: HCF of 132, 612, 285 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 132, 612, 285 using Euclid's Algorithm?
Answer: For arbitrary numbers 132, 612, 285 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.