Highest Common Factor of 128, 357, 213 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 128, 357, 213 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 128, 357, 213 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 128, 357, 213 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 128, 357, 213 is 1.
HCF(128, 357, 213) = 1
HCF of 128, 357, 213 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 128, 357, 213 is 1.
Highest Common Factor of 128,357,213 is 1
Step 1: Since 357 > 128, we apply the division lemma to 357 and 128, to get
357 = 128 x 2 + 101
Step 2: Since the reminder 128 ≠ 0, we apply division lemma to 101 and 128, to get
128 = 101 x 1 + 27
Step 3: We consider the new divisor 101 and the new remainder 27, and apply the division lemma to get
101 = 27 x 3 + 20
We consider the new divisor 27 and the new remainder 20,and apply the division lemma to get
27 = 20 x 1 + 7
We consider the new divisor 20 and the new remainder 7,and apply the division lemma to get
20 = 7 x 2 + 6
We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get
7 = 6 x 1 + 1
We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get
6 = 1 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 128 and 357 is 1
Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(27,20) = HCF(101,27) = HCF(128,101) = HCF(357,128) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 213 > 1, we apply the division lemma to 213 and 1, to get
213 = 1 x 213 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 213 is 1
Notice that 1 = HCF(213,1) .
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Frequently Asked Questions on HCF of 128, 357, 213 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 128, 357, 213?
Answer: HCF of 128, 357, 213 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 128, 357, 213 using Euclid's Algorithm?
Answer: For arbitrary numbers 128, 357, 213 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.