Highest Common Factor of 252, 687, 225 using Euclid's algorithm
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 252, 687, 225 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 252, 687, 225 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 252, 687, 225 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 252, 687, 225 is 3.
HCF(252, 687, 225) = 3
HCF of 252, 687, 225 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 252, 687, 225 is 3.
Highest Common Factor of 252,687,225 is 3
Step 1: Since 687 > 252, we apply the division lemma to 687 and 252, to get
687 = 252 x 2 + 183
Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 183 and 252, to get
252 = 183 x 1 + 69
Step 3: We consider the new divisor 183 and the new remainder 69, and apply the division lemma to get
183 = 69 x 2 + 45
We consider the new divisor 69 and the new remainder 45,and apply the division lemma to get
69 = 45 x 1 + 24
We consider the new divisor 45 and the new remainder 24,and apply the division lemma to get
45 = 24 x 1 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 252 and 687 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(69,45) = HCF(183,69) = HCF(252,183) = HCF(687,252) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 225 > 3, we apply the division lemma to 225 and 3, to get
225 = 3 x 75 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 225 is 3
Notice that 3 = HCF(225,3) .
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Frequently Asked Questions on HCF of 252, 687, 225 using Euclid's Algorithm
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 252, 687, 225?
Answer: HCF of 252, 687, 225 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 252, 687, 225 using Euclid's Algorithm?
Answer: For arbitrary numbers 252, 687, 225 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.