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 280, 500 i.e. 20 the largest integer that leaves a remainder zero for all numbers.
HCF of 280, 500 is 20 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 280, 500 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 280, 500 is 20.
HCF(280, 500) = 20
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 280, 500 is 20.
Step 1: Since 500 > 280, we apply the division lemma to 500 and 280, to get
500 = 280 x 1 + 220
Step 2: Since the reminder 280 ≠ 0, we apply division lemma to 220 and 280, to get
280 = 220 x 1 + 60
Step 3: We consider the new divisor 220 and the new remainder 60, and apply the division lemma to get
220 = 60 x 3 + 40
We consider the new divisor 60 and the new remainder 40,and apply the division lemma to get
60 = 40 x 1 + 20
We consider the new divisor 40 and the new remainder 20,and apply the division lemma to get
40 = 20 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 280 and 500 is 20
Notice that 20 = HCF(40,20) = HCF(60,40) = HCF(220,60) = HCF(280,220) = HCF(500,280) .
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 280, 500?
Answer: HCF of 280, 500 is 20 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 280, 500 using Euclid's Algorithm?
Answer: For arbitrary numbers 280, 500 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.