Highest Common Factor of 612, 1314 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 612, 1314 i.e. 18 the largest integer that leaves a remainder zero for all numbers.
HCF of 612, 1314 is 18 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 612, 1314 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 612, 1314 is 18.
HCF(612, 1314) = 18
HCF of 612, 1314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 612, 1314 is 18.
Highest Common Factor of 612,1314 is 18
Step 1: Since 1314 > 612, we apply the division lemma to 1314 and 612, to get
1314 = 612 x 2 + 90
Step 2: Since the reminder 612 ≠ 0, we apply division lemma to 90 and 612, to get
612 = 90 x 6 + 72
Step 3: We consider the new divisor 90 and the new remainder 72, and apply the division lemma to get
90 = 72 x 1 + 18
We consider the new divisor 72 and the new remainder 18, and apply the division lemma to get
72 = 18 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 18, the HCF of 612 and 1314 is 18
Notice that 18 = HCF(72,18) = HCF(90,72) = HCF(612,90) = HCF(1314,612) .
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Frequently Asked Questions on HCF of 612, 1314 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 612, 1314?
Answer: HCF of 612, 1314 is 18 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 612, 1314 using Euclid's Algorithm?
Answer: For arbitrary numbers 612, 1314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.