Highest Common Factor of 993, 174 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, 174 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 993, 174 is 3 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, 174 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, 174 is 3.
HCF(993, 174) = 3
HCF of 993, 174 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, 174 is 3.
Highest Common Factor of 993,174 is 3
Step 1: Since 993 > 174, we apply the division lemma to 993 and 174, to get
993 = 174 x 5 + 123
Step 2: Since the reminder 174 ≠ 0, we apply division lemma to 123 and 174, to get
174 = 123 x 1 + 51
Step 3: We consider the new divisor 123 and the new remainder 51, and apply the division lemma to get
123 = 51 x 2 + 21
We consider the new divisor 51 and the new remainder 21,and apply the division lemma to get
51 = 21 x 2 + 9
We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get
21 = 9 x 2 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get
9 = 3 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 993 and 174 is 3
Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(51,21) = HCF(123,51) = HCF(174,123) = HCF(993,174) .
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Frequently Asked Questions on HCF of 993, 174 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, 174?
Answer: HCF of 993, 174 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 993, 174 using Euclid's Algorithm?
Answer: For arbitrary numbers 993, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.