Highest Common Factor of 457, 714 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 457, 714 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 457, 714 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 457, 714 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 457, 714 is 1.
HCF(457, 714) = 1
HCF of 457, 714 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 457, 714 is 1.
Highest Common Factor of 457,714 is 1
Step 1: Since 714 > 457, we apply the division lemma to 714 and 457, to get
714 = 457 x 1 + 257
Step 2: Since the reminder 457 ≠ 0, we apply division lemma to 257 and 457, to get
457 = 257 x 1 + 200
Step 3: We consider the new divisor 257 and the new remainder 200, and apply the division lemma to get
257 = 200 x 1 + 57
We consider the new divisor 200 and the new remainder 57,and apply the division lemma to get
200 = 57 x 3 + 29
We consider the new divisor 57 and the new remainder 29,and apply the division lemma to get
57 = 29 x 1 + 28
We consider the new divisor 29 and the new remainder 28,and apply the division lemma to get
29 = 28 x 1 + 1
We consider the new divisor 28 and the new remainder 1,and apply the division lemma to get
28 = 1 x 28 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 457 and 714 is 1
Notice that 1 = HCF(28,1) = HCF(29,28) = HCF(57,29) = HCF(200,57) = HCF(257,200) = HCF(457,257) = HCF(714,457) .
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Frequently Asked Questions on HCF of 457, 714 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 457, 714?
Answer: HCF of 457, 714 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 457, 714 using Euclid's Algorithm?
Answer: For arbitrary numbers 457, 714 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.