Highest Common Factor of 172, 7804, 3966 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 172, 7804, 3966 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 172, 7804, 3966 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 172, 7804, 3966 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 172, 7804, 3966 is 2.
HCF(172, 7804, 3966) = 2
HCF of 172, 7804, 3966 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 172, 7804, 3966 is 2.
Highest Common Factor of 172,7804,3966 is 2
Step 1: Since 7804 > 172, we apply the division lemma to 7804 and 172, to get
7804 = 172 x 45 + 64
Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 64 and 172, to get
172 = 64 x 2 + 44
Step 3: We consider the new divisor 64 and the new remainder 44, and apply the division lemma to get
64 = 44 x 1 + 20
We consider the new divisor 44 and the new remainder 20,and apply the division lemma to get
44 = 20 x 2 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 172 and 7804 is 4
Notice that 4 = HCF(20,4) = HCF(44,20) = HCF(64,44) = HCF(172,64) = HCF(7804,172) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 3966 > 4, we apply the division lemma to 3966 and 4, to get
3966 = 4 x 991 + 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 3966 is 2
Notice that 2 = HCF(4,2) = HCF(3966,4) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 172, 7804, 3966 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 172, 7804, 3966?
Answer: HCF of 172, 7804, 3966 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 172, 7804, 3966 using Euclid's Algorithm?
Answer: For arbitrary numbers 172, 7804, 3966 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.