Highest Common Factor of 993, 557, 83 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 993, 557, 83 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 993, 557, 83 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 993, 557, 83 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 993, 557, 83 is 1.
HCF(993, 557, 83) = 1
HCF of 993, 557, 83 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 993, 557, 83 is 1.
Highest Common Factor of 993,557,83 is 1
Step 1: Since 993 > 557, we apply the division lemma to 993 and 557, to get
993 = 557 x 1 + 436
Step 2: Since the reminder 557 ≠ 0, we apply division lemma to 436 and 557, to get
557 = 436 x 1 + 121
Step 3: We consider the new divisor 436 and the new remainder 121, and apply the division lemma to get
436 = 121 x 3 + 73
We consider the new divisor 121 and the new remainder 73,and apply the division lemma to get
121 = 73 x 1 + 48
We consider the new divisor 73 and the new remainder 48,and apply the division lemma to get
73 = 48 x 1 + 25
We consider the new divisor 48 and the new remainder 25,and apply the division lemma to get
48 = 25 x 1 + 23
We consider the new divisor 25 and the new remainder 23,and apply the division lemma to get
25 = 23 x 1 + 2
We consider the new divisor 23 and the new remainder 2,and apply the division lemma to get
23 = 2 x 11 + 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 993 and 557 is 1
Notice that 1 = HCF(2,1) = HCF(23,2) = HCF(25,23) = HCF(48,25) = HCF(73,48) = HCF(121,73) = HCF(436,121) = HCF(557,436) = HCF(993,557) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 83 > 1, we apply the division lemma to 83 and 1, to get
83 = 1 x 83 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 83 is 1
Notice that 1 = HCF(83,1) .
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Frequently Asked Questions on HCF of 993, 557, 83 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 993, 557, 83?
Answer: HCF of 993, 557, 83 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 993, 557, 83 using Euclid's Algorithm?
Answer: For arbitrary numbers 993, 557, 83 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.