Highest Common Factor of 710, 275 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 710, 275 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 710, 275 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 710, 275 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 710, 275 is 5.
HCF(710, 275) = 5
HCF of 710, 275 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 710, 275 is 5.
Highest Common Factor of 710,275 is 5
Step 1: Since 710 > 275, we apply the division lemma to 710 and 275, to get
710 = 275 x 2 + 160
Step 2: Since the reminder 275 ≠ 0, we apply division lemma to 160 and 275, to get
275 = 160 x 1 + 115
Step 3: We consider the new divisor 160 and the new remainder 115, and apply the division lemma to get
160 = 115 x 1 + 45
We consider the new divisor 115 and the new remainder 45,and apply the division lemma to get
115 = 45 x 2 + 25
We consider the new divisor 45 and the new remainder 25,and apply the division lemma to get
45 = 25 x 1 + 20
We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get
25 = 20 x 1 + 5
We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get
20 = 5 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 710 and 275 is 5
Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(45,25) = HCF(115,45) = HCF(160,115) = HCF(275,160) = HCF(710,275) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 710, 275 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 710, 275?
Answer: HCF of 710, 275 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 710, 275 using Euclid's Algorithm?
Answer: For arbitrary numbers 710, 275 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.