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 6175, 2008 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6175, 2008 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 6175, 2008 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 6175, 2008 is 1.
HCF(6175, 2008) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6175, 2008 is 1.
Step 1: Since 6175 > 2008, we apply the division lemma to 6175 and 2008, to get
6175 = 2008 x 3 + 151
Step 2: Since the reminder 2008 ≠ 0, we apply division lemma to 151 and 2008, to get
2008 = 151 x 13 + 45
Step 3: We consider the new divisor 151 and the new remainder 45, and apply the division lemma to get
151 = 45 x 3 + 16
We consider the new divisor 45 and the new remainder 16,and apply the division lemma to get
45 = 16 x 2 + 13
We consider the new divisor 16 and the new remainder 13,and apply the division lemma to get
16 = 13 x 1 + 3
We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get
13 = 3 x 4 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6175 and 2008 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(16,13) = HCF(45,16) = HCF(151,45) = HCF(2008,151) = HCF(6175,2008) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 6175, 2008?
Answer: HCF of 6175, 2008 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6175, 2008 using Euclid's Algorithm?
Answer: For arbitrary numbers 6175, 2008 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.