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 872, 8219 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 872, 8219 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 872, 8219 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 872, 8219 is 1.
HCF(872, 8219) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 872, 8219 is 1.
Step 1: Since 8219 > 872, we apply the division lemma to 8219 and 872, to get
8219 = 872 x 9 + 371
Step 2: Since the reminder 872 ≠ 0, we apply division lemma to 371 and 872, to get
872 = 371 x 2 + 130
Step 3: We consider the new divisor 371 and the new remainder 130, and apply the division lemma to get
371 = 130 x 2 + 111
We consider the new divisor 130 and the new remainder 111,and apply the division lemma to get
130 = 111 x 1 + 19
We consider the new divisor 111 and the new remainder 19,and apply the division lemma to get
111 = 19 x 5 + 16
We consider the new divisor 19 and the new remainder 16,and apply the division lemma to get
19 = 16 x 1 + 3
We consider the new divisor 16 and the new remainder 3,and apply the division lemma to get
16 = 3 x 5 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 872 and 8219 is 1
Notice that 1 = HCF(3,1) = HCF(16,3) = HCF(19,16) = HCF(111,19) = HCF(130,111) = HCF(371,130) = HCF(872,371) = HCF(8219,872) .
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 872, 8219?
Answer: HCF of 872, 8219 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 872, 8219 using Euclid's Algorithm?
Answer: For arbitrary numbers 872, 8219 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.