Highest Common Factor of 320, 418, 165 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 320, 418, 165 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 320, 418, 165 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 320, 418, 165 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 320, 418, 165 is 1.
HCF(320, 418, 165) = 1
HCF of 320, 418, 165 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 320, 418, 165 is 1.
Highest Common Factor of 320,418,165 is 1
Step 1: Since 418 > 320, we apply the division lemma to 418 and 320, to get
418 = 320 x 1 + 98
Step 2: Since the reminder 320 ≠ 0, we apply division lemma to 98 and 320, to get
320 = 98 x 3 + 26
Step 3: We consider the new divisor 98 and the new remainder 26, and apply the division lemma to get
98 = 26 x 3 + 20
We consider the new divisor 26 and the new remainder 20,and apply the division lemma to get
26 = 20 x 1 + 6
We consider the new divisor 20 and the new remainder 6,and apply the division lemma to get
20 = 6 x 3 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 320 and 418 is 2
Notice that 2 = HCF(6,2) = HCF(20,6) = HCF(26,20) = HCF(98,26) = HCF(320,98) = HCF(418,320) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 165 > 2, we apply the division lemma to 165 and 2, to get
165 = 2 x 82 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 165 is 1
Notice that 1 = HCF(2,1) = HCF(165,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 320, 418, 165 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 320, 418, 165?
Answer: HCF of 320, 418, 165 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 320, 418, 165 using Euclid's Algorithm?
Answer: For arbitrary numbers 320, 418, 165 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.