Highest Common Factor of 360, 4146 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 360, 4146 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 360, 4146 is 6 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 360, 4146 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 360, 4146 is 6.
HCF(360, 4146) = 6
HCF of 360, 4146 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 360, 4146 is 6.
Highest Common Factor of 360,4146 is 6
Step 1: Since 4146 > 360, we apply the division lemma to 4146 and 360, to get
4146 = 360 x 11 + 186
Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 186 and 360, to get
360 = 186 x 1 + 174
Step 3: We consider the new divisor 186 and the new remainder 174, and apply the division lemma to get
186 = 174 x 1 + 12
We consider the new divisor 174 and the new remainder 12,and apply the division lemma to get
174 = 12 x 14 + 6
We consider the new divisor 12 and the new remainder 6,and apply the division lemma to get
12 = 6 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 360 and 4146 is 6
Notice that 6 = HCF(12,6) = HCF(174,12) = HCF(186,174) = HCF(360,186) = HCF(4146,360) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 360, 4146 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 360, 4146?
Answer: HCF of 360, 4146 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 360, 4146 using Euclid's Algorithm?
Answer: For arbitrary numbers 360, 4146 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.