Highest Common Factor of 165, 314, 240 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 165, 314, 240 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 165, 314, 240 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 165, 314, 240 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 165, 314, 240 is 1.
HCF(165, 314, 240) = 1
HCF of 165, 314, 240 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 165, 314, 240 is 1.
Highest Common Factor of 165,314,240 is 1
Step 1: Since 314 > 165, we apply the division lemma to 314 and 165, to get
314 = 165 x 1 + 149
Step 2: Since the reminder 165 ≠ 0, we apply division lemma to 149 and 165, to get
165 = 149 x 1 + 16
Step 3: We consider the new divisor 149 and the new remainder 16, and apply the division lemma to get
149 = 16 x 9 + 5
We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get
16 = 5 x 3 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 165 and 314 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(149,16) = HCF(165,149) = HCF(314,165) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 240 > 1, we apply the division lemma to 240 and 1, to get
240 = 1 x 240 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 240 is 1
Notice that 1 = HCF(240,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 165, 314, 240 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 165, 314, 240?
Answer: HCF of 165, 314, 240 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 165, 314, 240 using Euclid's Algorithm?
Answer: For arbitrary numbers 165, 314, 240 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.