Highest Common Factor of 3741, 8175 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 3741, 8175 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 3741, 8175 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 3741, 8175 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 3741, 8175 is 3.
HCF(3741, 8175) = 3
HCF of 3741, 8175 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3741, 8175 is 3.
Highest Common Factor of 3741,8175 is 3
Step 1: Since 8175 > 3741, we apply the division lemma to 8175 and 3741, to get
8175 = 3741 x 2 + 693
Step 2: Since the reminder 3741 ≠ 0, we apply division lemma to 693 and 3741, to get
3741 = 693 x 5 + 276
Step 3: We consider the new divisor 693 and the new remainder 276, and apply the division lemma to get
693 = 276 x 2 + 141
We consider the new divisor 276 and the new remainder 141,and apply the division lemma to get
276 = 141 x 1 + 135
We consider the new divisor 141 and the new remainder 135,and apply the division lemma to get
141 = 135 x 1 + 6
We consider the new divisor 135 and the new remainder 6,and apply the division lemma to get
135 = 6 x 22 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3741 and 8175 is 3
Notice that 3 = HCF(6,3) = HCF(135,6) = HCF(141,135) = HCF(276,141) = HCF(693,276) = HCF(3741,693) = HCF(8175,3741) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 3741, 8175 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 3741, 8175?
Answer: HCF of 3741, 8175 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3741, 8175 using Euclid's Algorithm?
Answer: For arbitrary numbers 3741, 8175 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.