Highest Common Factor of 105, 128, 180 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 105, 128, 180 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 105, 128, 180 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 105, 128, 180 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 105, 128, 180 is 1.
HCF(105, 128, 180) = 1
HCF of 105, 128, 180 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 105, 128, 180 is 1.
Highest Common Factor of 105,128,180 is 1
Step 1: Since 128 > 105, we apply the division lemma to 128 and 105, to get
128 = 105 x 1 + 23
Step 2: Since the reminder 105 ≠ 0, we apply division lemma to 23 and 105, to get
105 = 23 x 4 + 13
Step 3: We consider the new divisor 23 and the new remainder 13, and apply the division lemma to get
23 = 13 x 1 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 105 and 128 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(105,23) = HCF(128,105) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 180 > 1, we apply the division lemma to 180 and 1, to get
180 = 1 x 180 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 180 is 1
Notice that 1 = HCF(180,1) .
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Frequently Asked Questions on HCF of 105, 128, 180 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 105, 128, 180?
Answer: HCF of 105, 128, 180 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 105, 128, 180 using Euclid's Algorithm?
Answer: For arbitrary numbers 105, 128, 180 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
