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 384, 686, 129 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 384, 686, 129 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 384, 686, 129 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 384, 686, 129 is 1.
HCF(384, 686, 129) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 384, 686, 129 is 1.
Step 1: Since 686 > 384, we apply the division lemma to 686 and 384, to get
686 = 384 x 1 + 302
Step 2: Since the reminder 384 ≠ 0, we apply division lemma to 302 and 384, to get
384 = 302 x 1 + 82
Step 3: We consider the new divisor 302 and the new remainder 82, and apply the division lemma to get
302 = 82 x 3 + 56
We consider the new divisor 82 and the new remainder 56,and apply the division lemma to get
82 = 56 x 1 + 26
We consider the new divisor 56 and the new remainder 26,and apply the division lemma to get
56 = 26 x 2 + 4
We consider the new divisor 26 and the new remainder 4,and apply the division lemma to get
26 = 4 x 6 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 384 and 686 is 2
Notice that 2 = HCF(4,2) = HCF(26,4) = HCF(56,26) = HCF(82,56) = HCF(302,82) = HCF(384,302) = HCF(686,384) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 129 > 2, we apply the division lemma to 129 and 2, to get
129 = 2 x 64 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 129 is 1
Notice that 1 = HCF(2,1) = HCF(129,2) .
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 384, 686, 129?
Answer: HCF of 384, 686, 129 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 384, 686, 129 using Euclid's Algorithm?
Answer: For arbitrary numbers 384, 686, 129 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.