Highest Common Factor of 176, 128, 311 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 176, 128, 311 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 176, 128, 311 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 176, 128, 311 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 176, 128, 311 is 1.
HCF(176, 128, 311) = 1
HCF of 176, 128, 311 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 176, 128, 311 is 1.
Highest Common Factor of 176,128,311 is 1
Step 1: Since 176 > 128, we apply the division lemma to 176 and 128, to get
176 = 128 x 1 + 48
Step 2: Since the reminder 128 ≠ 0, we apply division lemma to 48 and 128, to get
128 = 48 x 2 + 32
Step 3: We consider the new divisor 48 and the new remainder 32, and apply the division lemma to get
48 = 32 x 1 + 16
We consider the new divisor 32 and the new remainder 16, and apply the division lemma to get
32 = 16 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 176 and 128 is 16
Notice that 16 = HCF(32,16) = HCF(48,32) = HCF(128,48) = HCF(176,128) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 311 > 16, we apply the division lemma to 311 and 16, to get
311 = 16 x 19 + 7
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 7 and 16, to get
16 = 7 x 2 + 2
Step 3: We consider the new divisor 7 and the new remainder 2, and apply the division lemma to get
7 = 2 x 3 + 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 16 and 311 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(311,16) .
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Frequently Asked Questions on HCF of 176, 128, 311 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 176, 128, 311?
Answer: HCF of 176, 128, 311 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 176, 128, 311 using Euclid's Algorithm?
Answer: For arbitrary numbers 176, 128, 311 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.