Highest Common Factor of 167, 21156 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 167, 21156 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 167, 21156 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 167, 21156 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 167, 21156 is 1.
HCF(167, 21156) = 1
HCF of 167, 21156 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 167, 21156 is 1.
Highest Common Factor of 167,21156 is 1
Step 1: Since 21156 > 167, we apply the division lemma to 21156 and 167, to get
21156 = 167 x 126 + 114
Step 2: Since the reminder 167 ≠ 0, we apply division lemma to 114 and 167, to get
167 = 114 x 1 + 53
Step 3: We consider the new divisor 114 and the new remainder 53, and apply the division lemma to get
114 = 53 x 2 + 8
We consider the new divisor 53 and the new remainder 8,and apply the division lemma to get
53 = 8 x 6 + 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 167 and 21156 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(53,8) = HCF(114,53) = HCF(167,114) = HCF(21156,167) .
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Frequently Asked Questions on HCF of 167, 21156 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 167, 21156?
Answer: HCF of 167, 21156 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 167, 21156 using Euclid's Algorithm?
Answer: For arbitrary numbers 167, 21156 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.