Highest Common Factor of 225, 3738, 8064 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 225, 3738, 8064 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 225, 3738, 8064 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 225, 3738, 8064 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 225, 3738, 8064 is 3.
HCF(225, 3738, 8064) = 3
HCF of 225, 3738, 8064 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 225, 3738, 8064 is 3.
Highest Common Factor of 225,3738,8064 is 3
Step 1: Since 3738 > 225, we apply the division lemma to 3738 and 225, to get
3738 = 225 x 16 + 138
Step 2: Since the reminder 225 ≠ 0, we apply division lemma to 138 and 225, to get
225 = 138 x 1 + 87
Step 3: We consider the new divisor 138 and the new remainder 87, and apply the division lemma to get
138 = 87 x 1 + 51
We consider the new divisor 87 and the new remainder 51,and apply the division lemma to get
87 = 51 x 1 + 36
We consider the new divisor 51 and the new remainder 36,and apply the division lemma to get
51 = 36 x 1 + 15
We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get
36 = 15 x 2 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 225 and 3738 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(51,36) = HCF(87,51) = HCF(138,87) = HCF(225,138) = HCF(3738,225) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 8064 > 3, we apply the division lemma to 8064 and 3, to get
8064 = 3 x 2688 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 8064 is 3
Notice that 3 = HCF(8064,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 225, 3738, 8064 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 225, 3738, 8064?
Answer: HCF of 225, 3738, 8064 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 225, 3738, 8064 using Euclid's Algorithm?
Answer: For arbitrary numbers 225, 3738, 8064 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.