Highest Common Factor of 214, 352, 997 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 214, 352, 997 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 214, 352, 997 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 214, 352, 997 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 214, 352, 997 is 1.
HCF(214, 352, 997) = 1
HCF of 214, 352, 997 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 214, 352, 997 is 1.
Highest Common Factor of 214,352,997 is 1
Step 1: Since 352 > 214, we apply the division lemma to 352 and 214, to get
352 = 214 x 1 + 138
Step 2: Since the reminder 214 ≠ 0, we apply division lemma to 138 and 214, to get
214 = 138 x 1 + 76
Step 3: We consider the new divisor 138 and the new remainder 76, and apply the division lemma to get
138 = 76 x 1 + 62
We consider the new divisor 76 and the new remainder 62,and apply the division lemma to get
76 = 62 x 1 + 14
We consider the new divisor 62 and the new remainder 14,and apply the division lemma to get
62 = 14 x 4 + 6
We consider the new divisor 14 and the new remainder 6,and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 214 and 352 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(62,14) = HCF(76,62) = HCF(138,76) = HCF(214,138) = HCF(352,214) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 997 > 2, we apply the division lemma to 997 and 2, to get
997 = 2 x 498 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 997 is 1
Notice that 1 = HCF(2,1) = HCF(997,2) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 214, 352, 997 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 214, 352, 997?
Answer: HCF of 214, 352, 997 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 214, 352, 997 using Euclid's Algorithm?
Answer: For arbitrary numbers 214, 352, 997 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.