Highest Common Factor of 2175, 7274 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 2175, 7274 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2175, 7274 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 2175, 7274 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 2175, 7274 is 1.
HCF(2175, 7274) = 1
HCF of 2175, 7274 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2175, 7274 is 1.
Highest Common Factor of 2175,7274 is 1
Step 1: Since 7274 > 2175, we apply the division lemma to 7274 and 2175, to get
7274 = 2175 x 3 + 749
Step 2: Since the reminder 2175 ≠ 0, we apply division lemma to 749 and 2175, to get
2175 = 749 x 2 + 677
Step 3: We consider the new divisor 749 and the new remainder 677, and apply the division lemma to get
749 = 677 x 1 + 72
We consider the new divisor 677 and the new remainder 72,and apply the division lemma to get
677 = 72 x 9 + 29
We consider the new divisor 72 and the new remainder 29,and apply the division lemma to get
72 = 29 x 2 + 14
We consider the new divisor 29 and the new remainder 14,and apply the division lemma to get
29 = 14 x 2 + 1
We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2175 and 7274 is 1
Notice that 1 = HCF(14,1) = HCF(29,14) = HCF(72,29) = HCF(677,72) = HCF(749,677) = HCF(2175,749) = HCF(7274,2175) .
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Frequently Asked Questions on HCF of 2175, 7274 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 2175, 7274?
Answer: HCF of 2175, 7274 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2175, 7274 using Euclid's Algorithm?
Answer: For arbitrary numbers 2175, 7274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.