Highest Common Factor of 3660, 8252, 85314 using Euclid's algorithm
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 3660, 8252, 85314 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 3660, 8252, 85314 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 3660, 8252, 85314 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 3660, 8252, 85314 is 2.
HCF(3660, 8252, 85314) = 2
HCF of 3660, 8252, 85314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 3660, 8252, 85314 is 2.
Highest Common Factor of 3660,8252,85314 is 2
Step 1: Since 8252 > 3660, we apply the division lemma to 8252 and 3660, to get
8252 = 3660 x 2 + 932
Step 2: Since the reminder 3660 ≠ 0, we apply division lemma to 932 and 3660, to get
3660 = 932 x 3 + 864
Step 3: We consider the new divisor 932 and the new remainder 864, and apply the division lemma to get
932 = 864 x 1 + 68
We consider the new divisor 864 and the new remainder 68,and apply the division lemma to get
864 = 68 x 12 + 48
We consider the new divisor 68 and the new remainder 48,and apply the division lemma to get
68 = 48 x 1 + 20
We consider the new divisor 48 and the new remainder 20,and apply the division lemma to get
48 = 20 x 2 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 3660 and 8252 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(48,20) = HCF(68,48) = HCF(864,68) = HCF(932,864) = HCF(3660,932) = HCF(8252,3660) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 85314 > 4, we apply the division lemma to 85314 and 4, to get
85314 = 4 x 21328 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, 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 4 and 85314 is 2
Notice that 2 = HCF(4,2) = HCF(85314,4) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 3660, 8252, 85314 using Euclid's Algorithm
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 3660, 8252, 85314?
Answer: HCF of 3660, 8252, 85314 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 3660, 8252, 85314 using Euclid's Algorithm?
Answer: For arbitrary numbers 3660, 8252, 85314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.