Highest Common Factor of 3756, 9645 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 3756, 9645 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 3756, 9645 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 3756, 9645 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 3756, 9645 is 3.
HCF(3756, 9645) = 3
HCF of 3756, 9645 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3756, 9645 is 3.
Highest Common Factor of 3756,9645 is 3
Step 1: Since 9645 > 3756, we apply the division lemma to 9645 and 3756, to get
9645 = 3756 x 2 + 2133
Step 2: Since the reminder 3756 ≠ 0, we apply division lemma to 2133 and 3756, to get
3756 = 2133 x 1 + 1623
Step 3: We consider the new divisor 2133 and the new remainder 1623, and apply the division lemma to get
2133 = 1623 x 1 + 510
We consider the new divisor 1623 and the new remainder 510,and apply the division lemma to get
1623 = 510 x 3 + 93
We consider the new divisor 510 and the new remainder 93,and apply the division lemma to get
510 = 93 x 5 + 45
We consider the new divisor 93 and the new remainder 45,and apply the division lemma to get
93 = 45 x 2 + 3
We consider the new divisor 45 and the new remainder 3,and apply the division lemma to get
45 = 3 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3756 and 9645 is 3
Notice that 3 = HCF(45,3) = HCF(93,45) = HCF(510,93) = HCF(1623,510) = HCF(2133,1623) = HCF(3756,2133) = HCF(9645,3756) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 3756, 9645 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 3756, 9645?
Answer: HCF of 3756, 9645 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3756, 9645 using Euclid's Algorithm?
Answer: For arbitrary numbers 3756, 9645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.