Highest Common Factor of 265, 500 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 265, 500 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 265, 500 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 265, 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 265, 500 is 5.
HCF(265, 500) = 5
HCF of 265, 500 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 265, 500 is 5.
Highest Common Factor of 265,500 is 5
Step 1: Since 500 > 265, we apply the division lemma to 500 and 265, to get
500 = 265 x 1 + 235
Step 2: Since the reminder 265 ≠ 0, we apply division lemma to 235 and 265, to get
265 = 235 x 1 + 30
Step 3: We consider the new divisor 235 and the new remainder 30, and apply the division lemma to get
235 = 30 x 7 + 25
We consider the new divisor 30 and the new remainder 25,and apply the division lemma to get
30 = 25 x 1 + 5
We consider the new divisor 25 and the new remainder 5,and apply the division lemma to get
25 = 5 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 265 and 500 is 5
Notice that 5 = HCF(25,5) = HCF(30,25) = HCF(235,30) = HCF(265,235) = HCF(500,265) .
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Frequently Asked Questions on HCF of 265, 500 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 265, 500?
Answer: HCF of 265, 500 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 265, 500 using Euclid's Algorithm?
Answer: For arbitrary numbers 265, 500 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
