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 9612, 9785 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 9612, 9785 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 9612, 9785 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 9612, 9785 is 1.
HCF(9612, 9785) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 9612, 9785 is 1.
Step 1: Since 9785 > 9612, we apply the division lemma to 9785 and 9612, to get
9785 = 9612 x 1 + 173
Step 2: Since the reminder 9612 ≠ 0, we apply division lemma to 173 and 9612, to get
9612 = 173 x 55 + 97
Step 3: We consider the new divisor 173 and the new remainder 97, and apply the division lemma to get
173 = 97 x 1 + 76
We consider the new divisor 97 and the new remainder 76,and apply the division lemma to get
97 = 76 x 1 + 21
We consider the new divisor 76 and the new remainder 21,and apply the division lemma to get
76 = 21 x 3 + 13
We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get
21 = 13 x 1 + 8
We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get
13 = 8 x 1 + 5
We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get
8 = 5 x 1 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 9612 and 9785 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(76,21) = HCF(97,76) = HCF(173,97) = HCF(9612,173) = HCF(9785,9612) .
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 9612, 9785?
Answer: HCF of 9612, 9785 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 9612, 9785 using Euclid's Algorithm?
Answer: For arbitrary numbers 9612, 9785 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.