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 265, 217, 280 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 265, 217, 280 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 265, 217, 280 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 265, 217, 280 is 1.
HCF(265, 217, 280) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 265, 217, 280 is 1.
Step 1: Since 265 > 217, we apply the division lemma to 265 and 217, to get
265 = 217 x 1 + 48
Step 2: Since the reminder 217 ≠ 0, we apply division lemma to 48 and 217, to get
217 = 48 x 4 + 25
Step 3: We consider the new divisor 48 and the new remainder 25, and apply the division lemma to get
48 = 25 x 1 + 23
We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get
25 = 23 x 1 + 2
We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get
23 = 2 x 11 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 265 and 217 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(48,25) = HCF(217,48) = HCF(265,217) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 280 > 1, we apply the division lemma to 280 and 1, to get
280 = 1 x 280 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 280 is 1
Notice that 1 = HCF(280,1) .
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 265, 217, 280?
Answer: HCF of 265, 217, 280 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 265, 217, 280 using Euclid's Algorithm?
Answer: For arbitrary numbers 265, 217, 280 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.