Highest Common Factor of 240, 609, 416 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 240, 609, 416 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 240, 609, 416 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 240, 609, 416 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 240, 609, 416 is 1.
HCF(240, 609, 416) = 1
HCF of 240, 609, 416 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 240, 609, 416 is 1.
Highest Common Factor of 240,609,416 is 1
Step 1: Since 609 > 240, we apply the division lemma to 609 and 240, to get
609 = 240 x 2 + 129
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 129 and 240, to get
240 = 129 x 1 + 111
Step 3: We consider the new divisor 129 and the new remainder 111, and apply the division lemma to get
129 = 111 x 1 + 18
We consider the new divisor 111 and the new remainder 18,and apply the division lemma to get
111 = 18 x 6 + 3
We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get
18 = 3 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 240 and 609 is 3
Notice that 3 = HCF(18,3) = HCF(111,18) = HCF(129,111) = HCF(240,129) = HCF(609,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 416 > 3, we apply the division lemma to 416 and 3, to get
416 = 3 x 138 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: We consider the new divisor 2 and the new remainder 1, and apply the division lemma 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 3 and 416 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(416,3) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 240, 609, 416 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 240, 609, 416?
Answer: HCF of 240, 609, 416 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 240, 609, 416 using Euclid's Algorithm?
Answer: For arbitrary numbers 240, 609, 416 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
