Highest Common Factor of 138, 440, 111 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 138, 440, 111 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 138, 440, 111 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 138, 440, 111 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 138, 440, 111 is 1.
HCF(138, 440, 111) = 1
HCF of 138, 440, 111 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 138, 440, 111 is 1.
Highest Common Factor of 138,440,111 is 1
Step 1: Since 440 > 138, we apply the division lemma to 440 and 138, to get
440 = 138 x 3 + 26
Step 2: Since the reminder 138 ≠ 0, we apply division lemma to 26 and 138, to get
138 = 26 x 5 + 8
Step 3: We consider the new divisor 26 and the new remainder 8, and apply the division lemma to get
26 = 8 x 3 + 2
We consider the new divisor 8 and the new remainder 2, and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 138 and 440 is 2
Notice that 2 = HCF(8,2) = HCF(26,8) = HCF(138,26) = HCF(440,138) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 111 > 2, we apply the division lemma to 111 and 2, to get
111 = 2 x 55 + 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 111 is 1
Notice that 1 = HCF(2,1) = HCF(111,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 138, 440, 111 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 138, 440, 111?
Answer: HCF of 138, 440, 111 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 138, 440, 111 using Euclid's Algorithm?
Answer: For arbitrary numbers 138, 440, 111 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.