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 7914, 6687, 43136 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 7914, 6687, 43136 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 7914, 6687, 43136 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 7914, 6687, 43136 is 1.
HCF(7914, 6687, 43136) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 7914, 6687, 43136 is 1.
Step 1: Since 7914 > 6687, we apply the division lemma to 7914 and 6687, to get
7914 = 6687 x 1 + 1227
Step 2: Since the reminder 6687 ≠ 0, we apply division lemma to 1227 and 6687, to get
6687 = 1227 x 5 + 552
Step 3: We consider the new divisor 1227 and the new remainder 552, and apply the division lemma to get
1227 = 552 x 2 + 123
We consider the new divisor 552 and the new remainder 123,and apply the division lemma to get
552 = 123 x 4 + 60
We consider the new divisor 123 and the new remainder 60,and apply the division lemma to get
123 = 60 x 2 + 3
We consider the new divisor 60 and the new remainder 3,and apply the division lemma to get
60 = 3 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 7914 and 6687 is 3
Notice that 3 = HCF(60,3) = HCF(123,60) = HCF(552,123) = HCF(1227,552) = HCF(6687,1227) = HCF(7914,6687) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 43136 > 3, we apply the division lemma to 43136 and 3, to get
43136 = 3 x 14378 + 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 43136 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(43136,3) .
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 7914, 6687, 43136?
Answer: HCF of 7914, 6687, 43136 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 7914, 6687, 43136 using Euclid's Algorithm?
Answer: For arbitrary numbers 7914, 6687, 43136 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.