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, 210, 325 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 660, 210, 325 is 5 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, 210, 325 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, 210, 325 is 5.
HCF(660, 210, 325) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 660, 210, 325 is 5.
Step 1: Since 660 > 210, we apply the division lemma to 660 and 210, to get
660 = 210 x 3 + 30
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 30 and 210, to get
210 = 30 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 30, the HCF of 660 and 210 is 30
Notice that 30 = HCF(210,30) = HCF(660,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 325 > 30, we apply the division lemma to 325 and 30, to get
325 = 30 x 10 + 25
Step 2: Since the reminder 30 ≠ 0, we apply division lemma to 25 and 30, to get
30 = 25 x 1 + 5
Step 3: We consider the new divisor 25 and the new remainder 5, and apply the division lemma to get
25 = 5 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 30 and 325 is 5
Notice that 5 = HCF(25,5) = HCF(30,25) = HCF(325,30) .
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, 210, 325?
Answer: HCF of 660, 210, 325 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 660, 210, 325 using Euclid's Algorithm?
Answer: For arbitrary numbers 660, 210, 325 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.