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 210, 280, 265 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 210, 280, 265 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 210, 280, 265 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 210, 280, 265 is 5.
HCF(210, 280, 265) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 210, 280, 265 is 5.
Step 1: Since 280 > 210, we apply the division lemma to 280 and 210, to get
280 = 210 x 1 + 70
Step 2: Since the reminder 210 ≠ 0, we apply division lemma to 70 and 210, to get
210 = 70 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 70, the HCF of 210 and 280 is 70
Notice that 70 = HCF(210,70) = HCF(280,210) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 265 > 70, we apply the division lemma to 265 and 70, to get
265 = 70 x 3 + 55
Step 2: Since the reminder 70 ≠ 0, we apply division lemma to 55 and 70, to get
70 = 55 x 1 + 15
Step 3: We consider the new divisor 55 and the new remainder 15, and apply the division lemma to get
55 = 15 x 3 + 10
We consider the new divisor 15 and the new remainder 10,and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 70 and 265 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(55,15) = HCF(70,55) = HCF(265,70) .
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 210, 280, 265?
Answer: HCF of 210, 280, 265 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 210, 280, 265 using Euclid's Algorithm?
Answer: For arbitrary numbers 210, 280, 265 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.