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 714, 419, 254 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 714, 419, 254 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 714, 419, 254 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 714, 419, 254 is 1.
HCF(714, 419, 254) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 714, 419, 254 is 1.
Step 1: Since 714 > 419, we apply the division lemma to 714 and 419, to get
714 = 419 x 1 + 295
Step 2: Since the reminder 419 ≠ 0, we apply division lemma to 295 and 419, to get
419 = 295 x 1 + 124
Step 3: We consider the new divisor 295 and the new remainder 124, and apply the division lemma to get
295 = 124 x 2 + 47
We consider the new divisor 124 and the new remainder 47,and apply the division lemma to get
124 = 47 x 2 + 30
We consider the new divisor 47 and the new remainder 30,and apply the division lemma to get
47 = 30 x 1 + 17
We consider the new divisor 30 and the new remainder 17,and apply the division lemma to get
30 = 17 x 1 + 13
We consider the new divisor 17 and the new remainder 13,and apply the division lemma to get
17 = 13 x 1 + 4
We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get
13 = 4 x 3 + 1
We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 714 and 419 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(17,13) = HCF(30,17) = HCF(47,30) = HCF(124,47) = HCF(295,124) = HCF(419,295) = HCF(714,419) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 254 > 1, we apply the division lemma to 254 and 1, to get
254 = 1 x 254 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 254 is 1
Notice that 1 = HCF(254,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 714, 419, 254?
Answer: HCF of 714, 419, 254 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 714, 419, 254 using Euclid's Algorithm?
Answer: For arbitrary numbers 714, 419, 254 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.