Highest Common Factor of 6138, 312 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 6138, 312 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 6138, 312 is 6 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 6138, 312 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 6138, 312 is 6.
HCF(6138, 312) = 6
HCF of 6138, 312 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 6138, 312 is 6.
Highest Common Factor of 6138,312 is 6
Step 1: Since 6138 > 312, we apply the division lemma to 6138 and 312, to get
6138 = 312 x 19 + 210
Step 2: Since the reminder 312 ≠ 0, we apply division lemma to 210 and 312, to get
312 = 210 x 1 + 102
Step 3: We consider the new divisor 210 and the new remainder 102, and apply the division lemma to get
210 = 102 x 2 + 6
We consider the new divisor 102 and the new remainder 6, and apply the division lemma to get
102 = 6 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 6138 and 312 is 6
Notice that 6 = HCF(102,6) = HCF(210,102) = HCF(312,210) = HCF(6138,312) .
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Frequently Asked Questions on HCF of 6138, 312 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 6138, 312?
Answer: HCF of 6138, 312 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 6138, 312 using Euclid's Algorithm?
Answer: For arbitrary numbers 6138, 312 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.