Highest Common Factor of 157, 2106 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, 2106 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 157, 2106 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, 2106 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, 2106 is 1.
HCF(157, 2106) = 1
HCF of 157, 2106 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, 2106 is 1.
Highest Common Factor of 157,2106 is 1
Step 1: Since 2106 > 157, we apply the division lemma to 2106 and 157, to get
2106 = 157 x 13 + 65
Step 2: Since the reminder 157 ≠ 0, we apply division lemma to 65 and 157, to get
157 = 65 x 2 + 27
Step 3: We consider the new divisor 65 and the new remainder 27, and apply the division lemma to get
65 = 27 x 2 + 11
We consider the new divisor 27 and the new remainder 11,and apply the division lemma to get
27 = 11 x 2 + 5
We consider the new divisor 11 and the new remainder 5,and apply the division lemma to get
11 = 5 x 2 + 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 157 and 2106 is 1
Notice that 1 = HCF(5,1) = HCF(11,5) = HCF(27,11) = HCF(65,27) = HCF(157,65) = HCF(2106,157) .
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Frequently Asked Questions on HCF of 157, 2106 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, 2106?
Answer: HCF of 157, 2106 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 157, 2106 using Euclid's Algorithm?
Answer: For arbitrary numbers 157, 2106 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.