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 6640, 2157 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 6640, 2157 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 6640, 2157 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 6640, 2157 is 1.
HCF(6640, 2157) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6640, 2157 is 1.
Step 1: Since 6640 > 2157, we apply the division lemma to 6640 and 2157, to get
6640 = 2157 x 3 + 169
Step 2: Since the reminder 2157 ≠ 0, we apply division lemma to 169 and 2157, to get
2157 = 169 x 12 + 129
Step 3: We consider the new divisor 169 and the new remainder 129, and apply the division lemma to get
169 = 129 x 1 + 40
We consider the new divisor 129 and the new remainder 40,and apply the division lemma to get
129 = 40 x 3 + 9
We consider the new divisor 40 and the new remainder 9,and apply the division lemma to get
40 = 9 x 4 + 4
We consider the new divisor 9 and the new remainder 4,and apply the division lemma to get
9 = 4 x 2 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6640 and 2157 is 1
Notice that 1 = HCF(4,1) = HCF(9,4) = HCF(40,9) = HCF(129,40) = HCF(169,129) = HCF(2157,169) = HCF(6640,2157) .
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 6640, 2157?
Answer: HCF of 6640, 2157 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6640, 2157 using Euclid's Algorithm?
Answer: For arbitrary numbers 6640, 2157 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.