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 3617, 645 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 3617, 645 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 3617, 645 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 3617, 645 is 1.
HCF(3617, 645) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3617, 645 is 1.
Step 1: Since 3617 > 645, we apply the division lemma to 3617 and 645, to get
3617 = 645 x 5 + 392
Step 2: Since the reminder 645 ≠ 0, we apply division lemma to 392 and 645, to get
645 = 392 x 1 + 253
Step 3: We consider the new divisor 392 and the new remainder 253, and apply the division lemma to get
392 = 253 x 1 + 139
We consider the new divisor 253 and the new remainder 139,and apply the division lemma to get
253 = 139 x 1 + 114
We consider the new divisor 139 and the new remainder 114,and apply the division lemma to get
139 = 114 x 1 + 25
We consider the new divisor 114 and the new remainder 25,and apply the division lemma to get
114 = 25 x 4 + 14
We consider the new divisor 25 and the new remainder 14,and apply the division lemma to get
25 = 14 x 1 + 11
We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get
14 = 11 x 1 + 3
We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get
11 = 3 x 3 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3617 and 645 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(25,14) = HCF(114,25) = HCF(139,114) = HCF(253,139) = HCF(392,253) = HCF(645,392) = HCF(3617,645) .
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 3617, 645?
Answer: HCF of 3617, 645 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3617, 645 using Euclid's Algorithm?
Answer: For arbitrary numbers 3617, 645 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.