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 636, 5138, 9752 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 636, 5138, 9752 is 2 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 636, 5138, 9752 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 636, 5138, 9752 is 2.
HCF(636, 5138, 9752) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 636, 5138, 9752 is 2.
Step 1: Since 5138 > 636, we apply the division lemma to 5138 and 636, to get
5138 = 636 x 8 + 50
Step 2: Since the reminder 636 ≠ 0, we apply division lemma to 50 and 636, to get
636 = 50 x 12 + 36
Step 3: We consider the new divisor 50 and the new remainder 36, and apply the division lemma to get
50 = 36 x 1 + 14
We consider the new divisor 36 and the new remainder 14,and apply the division lemma to get
36 = 14 x 2 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 636 and 5138 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(36,14) = HCF(50,36) = HCF(636,50) = HCF(5138,636) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 9752 > 2, we apply the division lemma to 9752 and 2, to get
9752 = 2 x 4876 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 9752 is 2
Notice that 2 = HCF(9752,2) .
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 636, 5138, 9752?
Answer: HCF of 636, 5138, 9752 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 636, 5138, 9752 using Euclid's Algorithm?
Answer: For arbitrary numbers 636, 5138, 9752 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.