Highest Common Factor of 157, 9688 using Euclid's algorithm
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 157, 9688 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 157, 9688 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 157, 9688 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 157, 9688 is 1.
HCF(157, 9688) = 1
HCF of 157, 9688 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 157, 9688 is 1.
Highest Common Factor of 157,9688 is 1
Step 1: Since 9688 > 157, we apply the division lemma to 9688 and 157, to get
9688 = 157 x 61 + 111
Step 2: Since the reminder 157 ≠ 0, we apply division lemma to 111 and 157, to get
157 = 111 x 1 + 46
Step 3: We consider the new divisor 111 and the new remainder 46, and apply the division lemma to get
111 = 46 x 2 + 19
We consider the new divisor 46 and the new remainder 19,and apply the division lemma to get
46 = 19 x 2 + 8
We consider the new divisor 19 and the new remainder 8,and apply the division lemma to get
19 = 8 x 2 + 3
We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get
8 = 3 x 2 + 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 157 and 9688 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(19,8) = HCF(46,19) = HCF(111,46) = HCF(157,111) = HCF(9688,157) .
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Frequently Asked Questions on HCF of 157, 9688 using Euclid's Algorithm
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 157, 9688?
Answer: HCF of 157, 9688 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 157, 9688 using Euclid's Algorithm?
Answer: For arbitrary numbers 157, 9688 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.