Highest Common Factor of 55, 40, 118 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 55, 40, 118 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 55, 40, 118 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 55, 40, 118 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 55, 40, 118 is 1.
HCF(55, 40, 118) = 1
HCF of 55, 40, 118 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 55, 40, 118 is 1.
Highest Common Factor of 55,40,118 is 1
Step 1: Since 55 > 40, we apply the division lemma to 55 and 40, to get
55 = 40 x 1 + 15
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 15 and 40, to get
40 = 15 x 2 + 10
Step 3: We consider the new divisor 15 and the new remainder 10, and apply the division lemma to get
15 = 10 x 1 + 5
We consider the new divisor 10 and the new remainder 5, and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 55 and 40 is 5
Notice that 5 = HCF(10,5) = HCF(15,10) = HCF(40,15) = HCF(55,40) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 118 > 5, we apply the division lemma to 118 and 5, to get
118 = 5 x 23 + 3
Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get
5 = 3 x 1 + 2
Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get
3 = 2 x 1 + 1
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 5 and 118 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(118,5) .
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Frequently Asked Questions on HCF of 55, 40, 118 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 55, 40, 118?
Answer: HCF of 55, 40, 118 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 55, 40, 118 using Euclid's Algorithm?
Answer: For arbitrary numbers 55, 40, 118 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.