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 8500, 5091 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 8500, 5091 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 8500, 5091 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 8500, 5091 is 1.
HCF(8500, 5091) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 8500, 5091 is 1.
Step 1: Since 8500 > 5091, we apply the division lemma to 8500 and 5091, to get
8500 = 5091 x 1 + 3409
Step 2: Since the reminder 5091 ≠ 0, we apply division lemma to 3409 and 5091, to get
5091 = 3409 x 1 + 1682
Step 3: We consider the new divisor 3409 and the new remainder 1682, and apply the division lemma to get
3409 = 1682 x 2 + 45
We consider the new divisor 1682 and the new remainder 45,and apply the division lemma to get
1682 = 45 x 37 + 17
We consider the new divisor 45 and the new remainder 17,and apply the division lemma to get
45 = 17 x 2 + 11
We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get
17 = 11 x 1 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8500 and 5091 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(45,17) = HCF(1682,45) = HCF(3409,1682) = HCF(5091,3409) = HCF(8500,5091) .
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 8500, 5091?
Answer: HCF of 8500, 5091 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 8500, 5091 using Euclid's Algorithm?
Answer: For arbitrary numbers 8500, 5091 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.