Highest Common Factor of 993, 172 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, 172 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 993, 172 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, 172 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, 172 is 1.
HCF(993, 172) = 1
HCF of 993, 172 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, 172 is 1.
Highest Common Factor of 993,172 is 1
Step 1: Since 993 > 172, we apply the division lemma to 993 and 172, to get
993 = 172 x 5 + 133
Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 133 and 172, to get
172 = 133 x 1 + 39
Step 3: We consider the new divisor 133 and the new remainder 39, and apply the division lemma to get
133 = 39 x 3 + 16
We consider the new divisor 39 and the new remainder 16,and apply the division lemma to get
39 = 16 x 2 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 172 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(39,16) = HCF(133,39) = HCF(172,133) = HCF(993,172) .
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Frequently Asked Questions on HCF of 993, 172 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, 172?
Answer: HCF of 993, 172 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 993, 172 using Euclid's Algorithm?
Answer: For arbitrary numbers 993, 172 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.