Highest Common Factor of 413, 448, 710 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 413, 448, 710 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 413, 448, 710 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 413, 448, 710 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 413, 448, 710 is 1.
HCF(413, 448, 710) = 1
HCF of 413, 448, 710 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 413, 448, 710 is 1.
Highest Common Factor of 413,448,710 is 1
Step 1: Since 448 > 413, we apply the division lemma to 448 and 413, to get
448 = 413 x 1 + 35
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 35 and 413, to get
413 = 35 x 11 + 28
Step 3: We consider the new divisor 35 and the new remainder 28, and apply the division lemma to get
35 = 28 x 1 + 7
We consider the new divisor 28 and the new remainder 7, and apply the division lemma to get
28 = 7 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 413 and 448 is 7
Notice that 7 = HCF(28,7) = HCF(35,28) = HCF(413,35) = HCF(448,413) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 710 > 7, we apply the division lemma to 710 and 7, to get
710 = 7 x 101 + 3
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 3 and 7, to get
7 = 3 x 2 + 1
Step 3: We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 710 is 1
Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(710,7) .
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Frequently Asked Questions on HCF of 413, 448, 710 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 413, 448, 710?
Answer: HCF of 413, 448, 710 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 413, 448, 710 using Euclid's Algorithm?
Answer: For arbitrary numbers 413, 448, 710 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.