Highest Common Factor of 176, 474, 60, 491 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, 474, 60, 491 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 176, 474, 60, 491 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, 474, 60, 491 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, 474, 60, 491 is 1.
HCF(176, 474, 60, 491) = 1
HCF of 176, 474, 60, 491 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, 474, 60, 491 is 1.
Highest Common Factor of 176,474,60,491 is 1
Step 1: Since 474 > 176, we apply the division lemma to 474 and 176, to get
474 = 176 x 2 + 122
Step 2: Since the reminder 176 ≠ 0, we apply division lemma to 122 and 176, to get
176 = 122 x 1 + 54
Step 3: We consider the new divisor 122 and the new remainder 54, and apply the division lemma to get
122 = 54 x 2 + 14
We consider the new divisor 54 and the new remainder 14,and apply the division lemma to get
54 = 14 x 3 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 176 and 474 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(54,14) = HCF(122,54) = HCF(176,122) = HCF(474,176) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 60 > 2, we apply the division lemma to 60 and 2, to get
60 = 2 x 30 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 60 is 2
Notice that 2 = HCF(60,2) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 491 > 2, we apply the division lemma to 491 and 2, to get
491 = 2 x 245 + 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 491 is 1
Notice that 1 = HCF(2,1) = HCF(491,2) .
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Frequently Asked Questions on HCF of 176, 474, 60, 491 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, 474, 60, 491?
Answer: HCF of 176, 474, 60, 491 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 176, 474, 60, 491 using Euclid's Algorithm?
Answer: For arbitrary numbers 176, 474, 60, 491 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.