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, 588, 116 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 387, 588, 116 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 387, 588, 116 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, 588, 116 is 1.
HCF(387, 588, 116) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 387, 588, 116 is 1.
Step 1: Since 588 > 387, we apply the division lemma to 588 and 387, to get
588 = 387 x 1 + 201
Step 2: Since the reminder 387 ≠ 0, we apply division lemma to 201 and 387, to get
387 = 201 x 1 + 186
Step 3: We consider the new divisor 201 and the new remainder 186, and apply the division lemma to get
201 = 186 x 1 + 15
We consider the new divisor 186 and the new remainder 15,and apply the division lemma to get
186 = 15 x 12 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 387 and 588 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(186,15) = HCF(201,186) = HCF(387,201) = HCF(588,387) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 116 > 3, we apply the division lemma to 116 and 3, to get
116 = 3 x 38 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 116 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(116,3) .
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, 588, 116?
Answer: HCF of 387, 588, 116 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 387, 588, 116 using Euclid's Algorithm?
Answer: For arbitrary numbers 387, 588, 116 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.