Highest Common Factor of 219, 391 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 219, 391 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 219, 391 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 219, 391 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 219, 391 is 1.
HCF(219, 391) = 1
HCF of 219, 391 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 219, 391 is 1.
Highest Common Factor of 219,391 is 1
Step 1: Since 391 > 219, we apply the division lemma to 391 and 219, to get
391 = 219 x 1 + 172
Step 2: Since the reminder 219 ≠ 0, we apply division lemma to 172 and 219, to get
219 = 172 x 1 + 47
Step 3: We consider the new divisor 172 and the new remainder 47, and apply the division lemma to get
172 = 47 x 3 + 31
We consider the new divisor 47 and the new remainder 31,and apply the division lemma to get
47 = 31 x 1 + 16
We consider the new divisor 31 and the new remainder 16,and apply the division lemma to get
31 = 16 x 1 + 15
We consider the new divisor 16 and the new remainder 15,and apply the division lemma to get
16 = 15 x 1 + 1
We consider the new divisor 15 and the new remainder 1,and apply the division lemma to get
15 = 1 x 15 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 219 and 391 is 1
Notice that 1 = HCF(15,1) = HCF(16,15) = HCF(31,16) = HCF(47,31) = HCF(172,47) = HCF(219,172) = HCF(391,219) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 219, 391 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 219, 391?
Answer: HCF of 219, 391 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 219, 391 using Euclid's Algorithm?
Answer: For arbitrary numbers 219, 391 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.