Highest Common Factor of 2058, 8176 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 2058, 8176 i.e. 14 the largest integer that leaves a remainder zero for all numbers.
HCF of 2058, 8176 is 14 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 2058, 8176 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 2058, 8176 is 14.
HCF(2058, 8176) = 14
HCF of 2058, 8176 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2058, 8176 is 14.
Highest Common Factor of 2058,8176 is 14
Step 1: Since 8176 > 2058, we apply the division lemma to 8176 and 2058, to get
8176 = 2058 x 3 + 2002
Step 2: Since the reminder 2058 ≠ 0, we apply division lemma to 2002 and 2058, to get
2058 = 2002 x 1 + 56
Step 3: We consider the new divisor 2002 and the new remainder 56, and apply the division lemma to get
2002 = 56 x 35 + 42
We consider the new divisor 56 and the new remainder 42,and apply the division lemma to get
56 = 42 x 1 + 14
We consider the new divisor 42 and the new remainder 14,and apply the division lemma to get
42 = 14 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 14, the HCF of 2058 and 8176 is 14
Notice that 14 = HCF(42,14) = HCF(56,42) = HCF(2002,56) = HCF(2058,2002) = HCF(8176,2058) .
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Frequently Asked Questions on HCF of 2058, 8176 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 2058, 8176?
Answer: HCF of 2058, 8176 is 14 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2058, 8176 using Euclid's Algorithm?
Answer: For arbitrary numbers 2058, 8176 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.