Highest Common Factor of 725, 470 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 725, 470 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 725, 470 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 725, 470 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 725, 470 is 5.
HCF(725, 470) = 5
HCF of 725, 470 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 725, 470 is 5.
Highest Common Factor of 725,470 is 5
Step 1: Since 725 > 470, we apply the division lemma to 725 and 470, to get
725 = 470 x 1 + 255
Step 2: Since the reminder 470 ≠ 0, we apply division lemma to 255 and 470, to get
470 = 255 x 1 + 215
Step 3: We consider the new divisor 255 and the new remainder 215, and apply the division lemma to get
255 = 215 x 1 + 40
We consider the new divisor 215 and the new remainder 40,and apply the division lemma to get
215 = 40 x 5 + 15
We consider the new divisor 40 and the new remainder 15,and apply the division lemma to get
40 = 15 x 2 + 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 725 and 470 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(215,40) = HCF(255,215) = HCF(470,255) = HCF(725,470) .
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Frequently Asked Questions on HCF of 725, 470 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 725, 470?
Answer: HCF of 725, 470 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 725, 470 using Euclid's Algorithm?
Answer: For arbitrary numbers 725, 470 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.