Highest Common Factor of 725, 274 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, 274 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 725, 274 is 1 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, 274 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, 274 is 1.
HCF(725, 274) = 1
HCF of 725, 274 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, 274 is 1.
Highest Common Factor of 725,274 is 1
Step 1: Since 725 > 274, we apply the division lemma to 725 and 274, to get
725 = 274 x 2 + 177
Step 2: Since the reminder 274 ≠ 0, we apply division lemma to 177 and 274, to get
274 = 177 x 1 + 97
Step 3: We consider the new divisor 177 and the new remainder 97, and apply the division lemma to get
177 = 97 x 1 + 80
We consider the new divisor 97 and the new remainder 80,and apply the division lemma to get
97 = 80 x 1 + 17
We consider the new divisor 80 and the new remainder 17,and apply the division lemma to get
80 = 17 x 4 + 12
We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get
17 = 12 x 1 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 725 and 274 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(80,17) = HCF(97,80) = HCF(177,97) = HCF(274,177) = HCF(725,274) .
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Frequently Asked Questions on HCF of 725, 274 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, 274?
Answer: HCF of 725, 274 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 725, 274 using Euclid's Algorithm?
Answer: For arbitrary numbers 725, 274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.