Highest Common Factor of 291, 188, 10, 314 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 291, 188, 10, 314 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 291, 188, 10, 314 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 291, 188, 10, 314 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 291, 188, 10, 314 is 1.
HCF(291, 188, 10, 314) = 1
HCF of 291, 188, 10, 314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 291, 188, 10, 314 is 1.
Highest Common Factor of 291,188,10,314 is 1
Step 1: Since 291 > 188, we apply the division lemma to 291 and 188, to get
291 = 188 x 1 + 103
Step 2: Since the reminder 188 ≠ 0, we apply division lemma to 103 and 188, to get
188 = 103 x 1 + 85
Step 3: We consider the new divisor 103 and the new remainder 85, and apply the division lemma to get
103 = 85 x 1 + 18
We consider the new divisor 85 and the new remainder 18,and apply the division lemma to get
85 = 18 x 4 + 13
We consider the new divisor 18 and the new remainder 13,and apply the division lemma to get
18 = 13 x 1 + 5
We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get
13 = 5 x 2 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 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 291 and 188 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(85,18) = HCF(103,85) = HCF(188,103) = HCF(291,188) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 10 > 1, we apply the division lemma to 10 and 1, to get
10 = 1 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 10 is 1
Notice that 1 = HCF(10,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 314 > 1, we apply the division lemma to 314 and 1, to get
314 = 1 x 314 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 314 is 1
Notice that 1 = HCF(314,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 291, 188, 10, 314 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 291, 188, 10, 314?
Answer: HCF of 291, 188, 10, 314 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 291, 188, 10, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 291, 188, 10, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.