Highest Common Factor of 420, 725 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 420, 725 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 725 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 420, 725 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 420, 725 is 5.
HCF(420, 725) = 5
HCF of 420, 725 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 725 is 5.
Highest Common Factor of 420,725 is 5
Step 1: Since 725 > 420, we apply the division lemma to 725 and 420, to get
725 = 420 x 1 + 305
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 305 and 420, to get
420 = 305 x 1 + 115
Step 3: We consider the new divisor 305 and the new remainder 115, and apply the division lemma to get
305 = 115 x 2 + 75
We consider the new divisor 115 and the new remainder 75,and apply the division lemma to get
115 = 75 x 1 + 40
We consider the new divisor 75 and the new remainder 40,and apply the division lemma to get
75 = 40 x 1 + 35
We consider the new divisor 40 and the new remainder 35,and apply the division lemma to get
40 = 35 x 1 + 5
We consider the new divisor 35 and the new remainder 5,and apply the division lemma to get
35 = 5 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 420 and 725 is 5
Notice that 5 = HCF(35,5) = HCF(40,35) = HCF(75,40) = HCF(115,75) = HCF(305,115) = HCF(420,305) = HCF(725,420) .
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Frequently Asked Questions on HCF of 420, 725 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 420, 725?
Answer: HCF of 420, 725 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 725 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 725 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
