Highest Common Factor of 605, 369, 32, 314 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 605, 369, 32, 314 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 605, 369, 32, 314 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 605, 369, 32, 314 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 605, 369, 32, 314 is 1.
HCF(605, 369, 32, 314) = 1
HCF of 605, 369, 32, 314 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 605, 369, 32, 314 is 1.
Highest Common Factor of 605,369,32,314 is 1
Step 1: Since 605 > 369, we apply the division lemma to 605 and 369, to get
605 = 369 x 1 + 236
Step 2: Since the reminder 369 ≠ 0, we apply division lemma to 236 and 369, to get
369 = 236 x 1 + 133
Step 3: We consider the new divisor 236 and the new remainder 133, and apply the division lemma to get
236 = 133 x 1 + 103
We consider the new divisor 133 and the new remainder 103,and apply the division lemma to get
133 = 103 x 1 + 30
We consider the new divisor 103 and the new remainder 30,and apply the division lemma to get
103 = 30 x 3 + 13
We consider the new divisor 30 and the new remainder 13,and apply the division lemma to get
30 = 13 x 2 + 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 605 and 369 is 1
Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(30,13) = HCF(103,30) = HCF(133,103) = HCF(236,133) = HCF(369,236) = HCF(605,369) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 32 > 1, we apply the division lemma to 32 and 1, to get
32 = 1 x 32 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 32 is 1
Notice that 1 = HCF(32,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 314 > 1, we apply the division lemma to 314 and 1, to get
314 = 1 x 314 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 314 is 1
Notice that 1 = HCF(314,1) .
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Frequently Asked Questions on HCF of 605, 369, 32, 314 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 605, 369, 32, 314?
Answer: HCF of 605, 369, 32, 314 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 605, 369, 32, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 605, 369, 32, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
