Highest Common Factor of 784, 16167 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, 16167 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 784, 16167 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, 16167 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, 16167 is 1.
HCF(784, 16167) = 1
HCF of 784, 16167 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, 16167 is 1.
Highest Common Factor of 784,16167 is 1
Step 1: Since 16167 > 784, we apply the division lemma to 16167 and 784, to get
16167 = 784 x 20 + 487
Step 2: Since the reminder 784 ≠ 0, we apply division lemma to 487 and 784, to get
784 = 487 x 1 + 297
Step 3: We consider the new divisor 487 and the new remainder 297, and apply the division lemma to get
487 = 297 x 1 + 190
We consider the new divisor 297 and the new remainder 190,and apply the division lemma to get
297 = 190 x 1 + 107
We consider the new divisor 190 and the new remainder 107,and apply the division lemma to get
190 = 107 x 1 + 83
We consider the new divisor 107 and the new remainder 83,and apply the division lemma to get
107 = 83 x 1 + 24
We consider the new divisor 83 and the new remainder 24,and apply the division lemma to get
83 = 24 x 3 + 11
We consider the new divisor 24 and the new remainder 11,and apply the division lemma to get
24 = 11 x 2 + 2
We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get
11 = 2 x 5 + 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 784 and 16167 is 1
Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(24,11) = HCF(83,24) = HCF(107,83) = HCF(190,107) = HCF(297,190) = HCF(487,297) = HCF(784,487) = HCF(16167,784) .
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Frequently Asked Questions on HCF of 784, 16167 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, 16167?
Answer: HCF of 784, 16167 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 784, 16167 using Euclid's Algorithm?
Answer: For arbitrary numbers 784, 16167 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.