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, 6512, 6972 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 225, 6512, 6972 is 1 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, 6512, 6972 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, 6512, 6972 is 1.
HCF(225, 6512, 6972) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 225, 6512, 6972 is 1.
Step 1: Since 6512 > 225, we apply the division lemma to 6512 and 225, to get
6512 = 225 x 28 + 212
Step 2: Since the reminder 225 ≠ 0, we apply division lemma to 212 and 225, to get
225 = 212 x 1 + 13
Step 3: We consider the new divisor 212 and the new remainder 13, and apply the division lemma to get
212 = 13 x 16 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 225 and 6512 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(212,13) = HCF(225,212) = HCF(6512,225) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6972 > 1, we apply the division lemma to 6972 and 1, to get
6972 = 1 x 6972 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6972 is 1
Notice that 1 = HCF(6972,1) .
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 225, 6512, 6972?
Answer: HCF of 225, 6512, 6972 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 225, 6512, 6972 using Euclid's Algorithm?
Answer: For arbitrary numbers 225, 6512, 6972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.