Highest Common Factor of 713, 413, 45, 298 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 713, 413, 45, 298 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 713, 413, 45, 298 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 713, 413, 45, 298 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 713, 413, 45, 298 is 1.
HCF(713, 413, 45, 298) = 1
HCF of 713, 413, 45, 298 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 713, 413, 45, 298 is 1.
Highest Common Factor of 713,413,45,298 is 1
Step 1: Since 713 > 413, we apply the division lemma to 713 and 413, to get
713 = 413 x 1 + 300
Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 300 and 413, to get
413 = 300 x 1 + 113
Step 3: We consider the new divisor 300 and the new remainder 113, and apply the division lemma to get
300 = 113 x 2 + 74
We consider the new divisor 113 and the new remainder 74,and apply the division lemma to get
113 = 74 x 1 + 39
We consider the new divisor 74 and the new remainder 39,and apply the division lemma to get
74 = 39 x 1 + 35
We consider the new divisor 39 and the new remainder 35,and apply the division lemma to get
39 = 35 x 1 + 4
We consider the new divisor 35 and the new remainder 4,and apply the division lemma to get
35 = 4 x 8 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
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 713 and 413 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(35,4) = HCF(39,35) = HCF(74,39) = HCF(113,74) = HCF(300,113) = HCF(413,300) = HCF(713,413) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 45 > 1, we apply the division lemma to 45 and 1, to get
45 = 1 x 45 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 45 is 1
Notice that 1 = HCF(45,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 298 > 1, we apply the division lemma to 298 and 1, to get
298 = 1 x 298 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 298 is 1
Notice that 1 = HCF(298,1) .
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Frequently Asked Questions on HCF of 713, 413, 45, 298 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 713, 413, 45, 298?
Answer: HCF of 713, 413, 45, 298 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 713, 413, 45, 298 using Euclid's Algorithm?
Answer: For arbitrary numbers 713, 413, 45, 298 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.