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 988, 6135, 4130 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 988, 6135, 4130 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 988, 6135, 4130 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 988, 6135, 4130 is 1.
HCF(988, 6135, 4130) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 988, 6135, 4130 is 1.
Step 1: Since 6135 > 988, we apply the division lemma to 6135 and 988, to get
6135 = 988 x 6 + 207
Step 2: Since the reminder 988 ≠ 0, we apply division lemma to 207 and 988, to get
988 = 207 x 4 + 160
Step 3: We consider the new divisor 207 and the new remainder 160, and apply the division lemma to get
207 = 160 x 1 + 47
We consider the new divisor 160 and the new remainder 47,and apply the division lemma to get
160 = 47 x 3 + 19
We consider the new divisor 47 and the new remainder 19,and apply the division lemma to get
47 = 19 x 2 + 9
We consider the new divisor 19 and the new remainder 9,and apply the division lemma to get
19 = 9 x 2 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 988 and 6135 is 1
Notice that 1 = HCF(9,1) = HCF(19,9) = HCF(47,19) = HCF(160,47) = HCF(207,160) = HCF(988,207) = HCF(6135,988) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 4130 > 1, we apply the division lemma to 4130 and 1, to get
4130 = 1 x 4130 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 4130 is 1
Notice that 1 = HCF(4130,1) .
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 988, 6135, 4130?
Answer: HCF of 988, 6135, 4130 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 988, 6135, 4130 using Euclid's Algorithm?
Answer: For arbitrary numbers 988, 6135, 4130 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.