Highest Common Factor of 2137, 3177 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 2137, 3177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2137, 3177 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 2137, 3177 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 2137, 3177 is 1.
HCF(2137, 3177) = 1
HCF of 2137, 3177 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2137, 3177 is 1.
Highest Common Factor of 2137,3177 is 1
Step 1: Since 3177 > 2137, we apply the division lemma to 3177 and 2137, to get
3177 = 2137 x 1 + 1040
Step 2: Since the reminder 2137 ≠ 0, we apply division lemma to 1040 and 2137, to get
2137 = 1040 x 2 + 57
Step 3: We consider the new divisor 1040 and the new remainder 57, and apply the division lemma to get
1040 = 57 x 18 + 14
We consider the new divisor 57 and the new remainder 14,and apply the division lemma to get
57 = 14 x 4 + 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 2137 and 3177 is 1
Notice that 1 = HCF(14,1) = HCF(57,14) = HCF(1040,57) = HCF(2137,1040) = HCF(3177,2137) .
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Frequently Asked Questions on HCF of 2137, 3177 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 2137, 3177?
Answer: HCF of 2137, 3177 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2137, 3177 using Euclid's Algorithm?
Answer: For arbitrary numbers 2137, 3177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.