Highest Common Factor of 2517, 1977 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 2517, 1977 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 2517, 1977 is 3 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 2517, 1977 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 2517, 1977 is 3.
HCF(2517, 1977) = 3
HCF of 2517, 1977 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2517, 1977 is 3.
Highest Common Factor of 2517,1977 is 3
Step 1: Since 2517 > 1977, we apply the division lemma to 2517 and 1977, to get
2517 = 1977 x 1 + 540
Step 2: Since the reminder 1977 ≠ 0, we apply division lemma to 540 and 1977, to get
1977 = 540 x 3 + 357
Step 3: We consider the new divisor 540 and the new remainder 357, and apply the division lemma to get
540 = 357 x 1 + 183
We consider the new divisor 357 and the new remainder 183,and apply the division lemma to get
357 = 183 x 1 + 174
We consider the new divisor 183 and the new remainder 174,and apply the division lemma to get
183 = 174 x 1 + 9
We consider the new divisor 174 and the new remainder 9,and apply the division lemma to get
174 = 9 x 19 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2517 and 1977 is 3
Notice that 3 = HCF(9,3) = HCF(174,9) = HCF(183,174) = HCF(357,183) = HCF(540,357) = HCF(1977,540) = HCF(2517,1977) .
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Frequently Asked Questions on HCF of 2517, 1977 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 2517, 1977?
Answer: HCF of 2517, 1977 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2517, 1977 using Euclid's Algorithm?
Answer: For arbitrary numbers 2517, 1977 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.