Highest Common Factor of 366, 991, 108, 11 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 366, 991, 108, 11 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 366, 991, 108, 11 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 366, 991, 108, 11 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 366, 991, 108, 11 is 1.
HCF(366, 991, 108, 11) = 1
HCF of 366, 991, 108, 11 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 366, 991, 108, 11 is 1.
Highest Common Factor of 366,991,108,11 is 1
Step 1: Since 991 > 366, we apply the division lemma to 991 and 366, to get
991 = 366 x 2 + 259
Step 2: Since the reminder 366 ≠ 0, we apply division lemma to 259 and 366, to get
366 = 259 x 1 + 107
Step 3: We consider the new divisor 259 and the new remainder 107, and apply the division lemma to get
259 = 107 x 2 + 45
We consider the new divisor 107 and the new remainder 45,and apply the division lemma to get
107 = 45 x 2 + 17
We consider the new divisor 45 and the new remainder 17,and apply the division lemma to get
45 = 17 x 2 + 11
We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get
17 = 11 x 1 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 366 and 991 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(45,17) = HCF(107,45) = HCF(259,107) = HCF(366,259) = HCF(991,366) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 108 > 1, we apply the division lemma to 108 and 1, to get
108 = 1 x 108 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 108 is 1
Notice that 1 = HCF(108,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 11 > 1, we apply the division lemma to 11 and 1, to get
11 = 1 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 11 is 1
Notice that 1 = HCF(11,1) .
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Frequently Asked Questions on HCF of 366, 991, 108, 11 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 366, 991, 108, 11?
Answer: HCF of 366, 991, 108, 11 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 366, 991, 108, 11 using Euclid's Algorithm?
Answer: For arbitrary numbers 366, 991, 108, 11 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.