Highest Common Factor of 100, 105, 125, 128 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 100, 105, 125, 128 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 100, 105, 125, 128 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 100, 105, 125, 128 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 100, 105, 125, 128 is 1.
HCF(100, 105, 125, 128) = 1
HCF of 100, 105, 125, 128 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 100, 105, 125, 128 is 1.
Highest Common Factor of 100,105,125,128 is 1
Step 1: Since 105 > 100, we apply the division lemma to 105 and 100, to get
105 = 100 x 1 + 5
Step 2: Since the reminder 100 ≠ 0, we apply division lemma to 5 and 100, to get
100 = 5 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 100 and 105 is 5
Notice that 5 = HCF(100,5) = HCF(105,100) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 125 > 5, we apply the division lemma to 125 and 5, to get
125 = 5 x 25 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 5 and 125 is 5
Notice that 5 = HCF(125,5) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 128 > 5, we apply the division lemma to 128 and 5, to get
128 = 5 x 25 + 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 128 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(128,5) .
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Frequently Asked Questions on HCF of 100, 105, 125, 128 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 100, 105, 125, 128?
Answer: HCF of 100, 105, 125, 128 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 100, 105, 125, 128 using Euclid's Algorithm?
Answer: For arbitrary numbers 100, 105, 125, 128 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
