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 387, 912, 513 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 387, 912, 513 is 3 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 387, 912, 513 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 387, 912, 513 is 3.
HCF(387, 912, 513) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 387, 912, 513 is 3.
Step 1: Since 912 > 387, we apply the division lemma to 912 and 387, to get
912 = 387 x 2 + 138
Step 2: Since the reminder 387 ≠ 0, we apply division lemma to 138 and 387, to get
387 = 138 x 2 + 111
Step 3: We consider the new divisor 138 and the new remainder 111, and apply the division lemma to get
138 = 111 x 1 + 27
We consider the new divisor 111 and the new remainder 27,and apply the division lemma to get
111 = 27 x 4 + 3
We consider the new divisor 27 and the new remainder 3,and apply the division lemma to get
27 = 3 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 387 and 912 is 3
Notice that 3 = HCF(27,3) = HCF(111,27) = HCF(138,111) = HCF(387,138) = HCF(912,387) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 513 > 3, we apply the division lemma to 513 and 3, to get
513 = 3 x 171 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 513 is 3
Notice that 3 = HCF(513,3) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 387, 912, 513?
Answer: HCF of 387, 912, 513 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 387, 912, 513 using Euclid's Algorithm?
Answer: For arbitrary numbers 387, 912, 513 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.