Highest Common Factor of 117, 191, 372 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 117, 191, 372 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 117, 191, 372 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 117, 191, 372 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 117, 191, 372 is 1.
HCF(117, 191, 372) = 1
HCF of 117, 191, 372 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 117, 191, 372 is 1.
Highest Common Factor of 117,191,372 is 1
Step 1: Since 191 > 117, we apply the division lemma to 191 and 117, to get
191 = 117 x 1 + 74
Step 2: Since the reminder 117 ≠ 0, we apply division lemma to 74 and 117, to get
117 = 74 x 1 + 43
Step 3: We consider the new divisor 74 and the new remainder 43, and apply the division lemma to get
74 = 43 x 1 + 31
We consider the new divisor 43 and the new remainder 31,and apply the division lemma to get
43 = 31 x 1 + 12
We consider the new divisor 31 and the new remainder 12,and apply the division lemma to get
31 = 12 x 2 + 7
We consider the new divisor 12 and the new remainder 7,and apply the division lemma to get
12 = 7 x 1 + 5
We consider the new divisor 7 and the new remainder 5,and apply the division lemma to get
7 = 5 x 1 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 117 and 191 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(12,7) = HCF(31,12) = HCF(43,31) = HCF(74,43) = HCF(117,74) = HCF(191,117) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 372 > 1, we apply the division lemma to 372 and 1, to get
372 = 1 x 372 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 372 is 1
Notice that 1 = HCF(372,1) .
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Frequently Asked Questions on HCF of 117, 191, 372 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 117, 191, 372?
Answer: HCF of 117, 191, 372 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 117, 191, 372 using Euclid's Algorithm?
Answer: For arbitrary numbers 117, 191, 372 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.