Highest Common Factor of 240, 336, 115 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, 336, 115 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 240, 336, 115 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, 336, 115 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, 336, 115 is 1.
HCF(240, 336, 115) = 1
HCF of 240, 336, 115 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, 336, 115 is 1.
Highest Common Factor of 240,336,115 is 1
Step 1: Since 336 > 240, we apply the division lemma to 336 and 240, to get
336 = 240 x 1 + 96
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 96 and 240, to get
240 = 96 x 2 + 48
Step 3: We consider the new divisor 96 and the new remainder 48, and apply the division lemma to get
96 = 48 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 48, the HCF of 240 and 336 is 48
Notice that 48 = HCF(96,48) = HCF(240,96) = HCF(336,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 115 > 48, we apply the division lemma to 115 and 48, to get
115 = 48 x 2 + 19
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 19 and 48, to get
48 = 19 x 2 + 10
Step 3: We consider the new divisor 19 and the new remainder 10, and apply the division lemma to get
19 = 10 x 1 + 9
We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get
10 = 9 x 1 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 48 and 115 is 1
Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(19,10) = HCF(48,19) = HCF(115,48) .
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Frequently Asked Questions on HCF of 240, 336, 115 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, 336, 115?
Answer: HCF of 240, 336, 115 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 240, 336, 115 using Euclid's Algorithm?
Answer: For arbitrary numbers 240, 336, 115 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.