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 851, 13085 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 851, 13085 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 851, 13085 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 851, 13085 is 1.
HCF(851, 13085) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 851, 13085 is 1.
Step 1: Since 13085 > 851, we apply the division lemma to 13085 and 851, to get
13085 = 851 x 15 + 320
Step 2: Since the reminder 851 ≠ 0, we apply division lemma to 320 and 851, to get
851 = 320 x 2 + 211
Step 3: We consider the new divisor 320 and the new remainder 211, and apply the division lemma to get
320 = 211 x 1 + 109
We consider the new divisor 211 and the new remainder 109,and apply the division lemma to get
211 = 109 x 1 + 102
We consider the new divisor 109 and the new remainder 102,and apply the division lemma to get
109 = 102 x 1 + 7
We consider the new divisor 102 and the new remainder 7,and apply the division lemma to get
102 = 7 x 14 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 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 851 and 13085 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(102,7) = HCF(109,102) = HCF(211,109) = HCF(320,211) = HCF(851,320) = HCF(13085,851) .
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 851, 13085?
Answer: HCF of 851, 13085 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 851, 13085 using Euclid's Algorithm?
Answer: For arbitrary numbers 851, 13085 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.