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 6870, 3538 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 6870, 3538 is 2 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 6870, 3538 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 6870, 3538 is 2.
HCF(6870, 3538) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6870, 3538 is 2.
Step 1: Since 6870 > 3538, we apply the division lemma to 6870 and 3538, to get
6870 = 3538 x 1 + 3332
Step 2: Since the reminder 3538 ≠ 0, we apply division lemma to 3332 and 3538, to get
3538 = 3332 x 1 + 206
Step 3: We consider the new divisor 3332 and the new remainder 206, and apply the division lemma to get
3332 = 206 x 16 + 36
We consider the new divisor 206 and the new remainder 36,and apply the division lemma to get
206 = 36 x 5 + 26
We consider the new divisor 36 and the new remainder 26,and apply the division lemma to get
36 = 26 x 1 + 10
We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get
26 = 10 x 2 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6870 and 3538 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(36,26) = HCF(206,36) = HCF(3332,206) = HCF(3538,3332) = HCF(6870,3538) .
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 6870, 3538?
Answer: HCF of 6870, 3538 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6870, 3538 using Euclid's Algorithm?
Answer: For arbitrary numbers 6870, 3538 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.