Highest Common Factor of 414, 229, 122, 214 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 414, 229, 122, 214 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 229, 122, 214 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 414, 229, 122, 214 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 414, 229, 122, 214 is 1.
HCF(414, 229, 122, 214) = 1
HCF of 414, 229, 122, 214 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 229, 122, 214 is 1.
Highest Common Factor of 414,229,122,214 is 1
Step 1: Since 414 > 229, we apply the division lemma to 414 and 229, to get
414 = 229 x 1 + 185
Step 2: Since the reminder 229 ≠ 0, we apply division lemma to 185 and 229, to get
229 = 185 x 1 + 44
Step 3: We consider the new divisor 185 and the new remainder 44, and apply the division lemma to get
185 = 44 x 4 + 9
We consider the new divisor 44 and the new remainder 9,and apply the division lemma to get
44 = 9 x 4 + 8
We consider the new divisor 9 and the new remainder 8,and apply the division lemma to get
9 = 8 x 1 + 1
We consider the new divisor 8 and the new remainder 1,and apply the division lemma to get
8 = 1 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 414 and 229 is 1
Notice that 1 = HCF(8,1) = HCF(9,8) = HCF(44,9) = HCF(185,44) = HCF(229,185) = HCF(414,229) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 122 > 1, we apply the division lemma to 122 and 1, to get
122 = 1 x 122 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 122 is 1
Notice that 1 = HCF(122,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 214 > 1, we apply the division lemma to 214 and 1, to get
214 = 1 x 214 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 214 is 1
Notice that 1 = HCF(214,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 414, 229, 122, 214 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 414, 229, 122, 214?
Answer: HCF of 414, 229, 122, 214 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 229, 122, 214 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 229, 122, 214 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.