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 660, 405, 285 i.e. 15 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 405, 285 is 15 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 660, 405, 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 660, 405, 285 is 15.
HCF(660, 405, 285) = 15
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 405, 285 is 15.
Step 1: Since 660 > 405, we apply the division lemma to 660 and 405, to get
660 = 405 x 1 + 255
Step 2: Since the reminder 405 ≠ 0, we apply division lemma to 255 and 405, to get
405 = 255 x 1 + 150
Step 3: We consider the new divisor 255 and the new remainder 150, and apply the division lemma to get
255 = 150 x 1 + 105
We consider the new divisor 150 and the new remainder 105,and apply the division lemma to get
150 = 105 x 1 + 45
We consider the new divisor 105 and the new remainder 45,and apply the division lemma to get
105 = 45 x 2 + 15
We consider the new divisor 45 and the new remainder 15,and apply the division lemma to get
45 = 15 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 660 and 405 is 15
Notice that 15 = HCF(45,15) = HCF(105,45) = HCF(150,105) = HCF(255,150) = HCF(405,255) = HCF(660,405) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 285 > 15, we apply the division lemma to 285 and 15, to get
285 = 15 x 19 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 15, the HCF of 15 and 285 is 15
Notice that 15 = HCF(285,15) .
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 660, 405, 285?
Answer: HCF of 660, 405, 285 is 15 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 405, 285 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 405, 285 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.