Highest Common Factor of 2174, 1531 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 2174, 1531 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2174, 1531 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 2174, 1531 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 2174, 1531 is 1.
HCF(2174, 1531) = 1
HCF of 2174, 1531 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2174, 1531 is 1.
Highest Common Factor of 2174,1531 is 1
Step 1: Since 2174 > 1531, we apply the division lemma to 2174 and 1531, to get
2174 = 1531 x 1 + 643
Step 2: Since the reminder 1531 ≠ 0, we apply division lemma to 643 and 1531, to get
1531 = 643 x 2 + 245
Step 3: We consider the new divisor 643 and the new remainder 245, and apply the division lemma to get
643 = 245 x 2 + 153
We consider the new divisor 245 and the new remainder 153,and apply the division lemma to get
245 = 153 x 1 + 92
We consider the new divisor 153 and the new remainder 92,and apply the division lemma to get
153 = 92 x 1 + 61
We consider the new divisor 92 and the new remainder 61,and apply the division lemma to get
92 = 61 x 1 + 31
We consider the new divisor 61 and the new remainder 31,and apply the division lemma to get
61 = 31 x 1 + 30
We consider the new divisor 31 and the new remainder 30,and apply the division lemma to get
31 = 30 x 1 + 1
We consider the new divisor 30 and the new remainder 1,and apply the division lemma to get
30 = 1 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2174 and 1531 is 1
Notice that 1 = HCF(30,1) = HCF(31,30) = HCF(61,31) = HCF(92,61) = HCF(153,92) = HCF(245,153) = HCF(643,245) = HCF(1531,643) = HCF(2174,1531) .
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Frequently Asked Questions on HCF of 2174, 1531 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 2174, 1531?
Answer: HCF of 2174, 1531 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2174, 1531 using Euclid's Algorithm?
Answer: For arbitrary numbers 2174, 1531 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.