Highest Common Factor of 491, 188, 38 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 491, 188, 38 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 491, 188, 38 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 491, 188, 38 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 491, 188, 38 is 1.
HCF(491, 188, 38) = 1
HCF of 491, 188, 38 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 491, 188, 38 is 1.
Highest Common Factor of 491,188,38 is 1
Step 1: Since 491 > 188, we apply the division lemma to 491 and 188, to get
491 = 188 x 2 + 115
Step 2: Since the reminder 188 ≠ 0, we apply division lemma to 115 and 188, to get
188 = 115 x 1 + 73
Step 3: We consider the new divisor 115 and the new remainder 73, and apply the division lemma to get
115 = 73 x 1 + 42
We consider the new divisor 73 and the new remainder 42,and apply the division lemma to get
73 = 42 x 1 + 31
We consider the new divisor 42 and the new remainder 31,and apply the division lemma to get
42 = 31 x 1 + 11
We consider the new divisor 31 and the new remainder 11,and apply the division lemma to get
31 = 11 x 2 + 9
We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get
11 = 9 x 1 + 2
We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get
9 = 2 x 4 + 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 491 and 188 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(31,11) = HCF(42,31) = HCF(73,42) = HCF(115,73) = HCF(188,115) = HCF(491,188) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 38 > 1, we apply the division lemma to 38 and 1, to get
38 = 1 x 38 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 38 is 1
Notice that 1 = HCF(38,1) .
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Frequently Asked Questions on HCF of 491, 188, 38 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 491, 188, 38?
Answer: HCF of 491, 188, 38 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 491, 188, 38 using Euclid's Algorithm?
Answer: For arbitrary numbers 491, 188, 38 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.