Highest Common Factor of 784, 9625, 2105 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 784, 9625, 2105 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 784, 9625, 2105 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 784, 9625, 2105 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 784, 9625, 2105 is 1.
HCF(784, 9625, 2105) = 1
HCF of 784, 9625, 2105 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 784, 9625, 2105 is 1.
Highest Common Factor of 784,9625,2105 is 1
Step 1: Since 9625 > 784, we apply the division lemma to 9625 and 784, to get
9625 = 784 x 12 + 217
Step 2: Since the reminder 784 ≠ 0, we apply division lemma to 217 and 784, to get
784 = 217 x 3 + 133
Step 3: We consider the new divisor 217 and the new remainder 133, and apply the division lemma to get
217 = 133 x 1 + 84
We consider the new divisor 133 and the new remainder 84,and apply the division lemma to get
133 = 84 x 1 + 49
We consider the new divisor 84 and the new remainder 49,and apply the division lemma to get
84 = 49 x 1 + 35
We consider the new divisor 49 and the new remainder 35,and apply the division lemma to get
49 = 35 x 1 + 14
We consider the new divisor 35 and the new remainder 14,and apply the division lemma to get
35 = 14 x 2 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 784 and 9625 is 7
Notice that 7 = HCF(14,7) = HCF(35,14) = HCF(49,35) = HCF(84,49) = HCF(133,84) = HCF(217,133) = HCF(784,217) = HCF(9625,784) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 2105 > 7, we apply the division lemma to 2105 and 7, to get
2105 = 7 x 300 + 5
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 5 and 7, to get
7 = 5 x 1 + 2
Step 3: We consider the new divisor 5 and the new remainder 2, and apply the division lemma to get
5 = 2 x 2 + 1
We consider the new divisor 2 and the new remainder 1, and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 2105 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(7,5) = HCF(2105,7) .
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Frequently Asked Questions on HCF of 784, 9625, 2105 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 784, 9625, 2105?
Answer: HCF of 784, 9625, 2105 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 784, 9625, 2105 using Euclid's Algorithm?
Answer: For arbitrary numbers 784, 9625, 2105 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.