Highest Common Factor of 300, 784, 493 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 300, 784, 493 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 300, 784, 493 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 300, 784, 493 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 300, 784, 493 is 1.
HCF(300, 784, 493) = 1
HCF of 300, 784, 493 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 300, 784, 493 is 1.
Highest Common Factor of 300,784,493 is 1
Step 1: Since 784 > 300, we apply the division lemma to 784 and 300, to get
784 = 300 x 2 + 184
Step 2: Since the reminder 300 ≠ 0, we apply division lemma to 184 and 300, to get
300 = 184 x 1 + 116
Step 3: We consider the new divisor 184 and the new remainder 116, and apply the division lemma to get
184 = 116 x 1 + 68
We consider the new divisor 116 and the new remainder 68,and apply the division lemma to get
116 = 68 x 1 + 48
We consider the new divisor 68 and the new remainder 48,and apply the division lemma to get
68 = 48 x 1 + 20
We consider the new divisor 48 and the new remainder 20,and apply the division lemma to get
48 = 20 x 2 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 300 and 784 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(48,20) = HCF(68,48) = HCF(116,68) = HCF(184,116) = HCF(300,184) = HCF(784,300) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 493 > 4, we apply the division lemma to 493 and 4, to get
493 = 4 x 123 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, 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 4 and 493 is 1
Notice that 1 = HCF(4,1) = HCF(493,4) .
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Frequently Asked Questions on HCF of 300, 784, 493 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 300, 784, 493?
Answer: HCF of 300, 784, 493 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 300, 784, 493 using Euclid's Algorithm?
Answer: For arbitrary numbers 300, 784, 493 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.