Highest Common Factor of 312, 2167 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 312, 2167 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 312, 2167 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 312, 2167 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 312, 2167 is 1.
HCF(312, 2167) = 1
HCF of 312, 2167 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 312, 2167 is 1.
Highest Common Factor of 312,2167 is 1
Step 1: Since 2167 > 312, we apply the division lemma to 2167 and 312, to get
2167 = 312 x 6 + 295
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 295 and 312, to get
312 = 295 x 1 + 17
Step 3: We consider the new divisor 295 and the new remainder 17, and apply the division lemma to get
295 = 17 x 17 + 6
We consider the new divisor 17 and the new remainder 6,and apply the division lemma to get
17 = 6 x 2 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 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 312 and 2167 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(17,6) = HCF(295,17) = HCF(312,295) = HCF(2167,312) .
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Frequently Asked Questions on HCF of 312, 2167 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 312, 2167?
Answer: HCF of 312, 2167 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 312, 2167 using Euclid's Algorithm?
Answer: For arbitrary numbers 312, 2167 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.