Highest Common Factor of 99, 72, 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 99, 72, 174 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 99, 72, 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 99, 72, 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 99, 72, 174 is 3.
HCF(99, 72, 174) = 3
HCF of 99, 72, 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 99, 72, 174 is 3.
Highest Common Factor of 99,72,174 is 3
Step 1: Since 99 > 72, we apply the division lemma to 99 and 72, to get
99 = 72 x 1 + 27
Step 2: Since the reminder 72 ≠ 0, we apply division lemma to 27 and 72, to get
72 = 27 x 2 + 18
Step 3: We consider the new divisor 27 and the new remainder 18, and apply the division lemma to get
27 = 18 x 1 + 9
We consider the new divisor 18 and the new remainder 9, and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 99 and 72 is 9
Notice that 9 = HCF(18,9) = HCF(27,18) = HCF(72,27) = HCF(99,72) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 174 > 9, we apply the division lemma to 174 and 9, to get
174 = 9 x 19 + 3
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 3 and 9, 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 9 and 174 is 3
Notice that 3 = HCF(9,3) = HCF(174,9) .
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Frequently Asked Questions on HCF of 99, 72, 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 99, 72, 174?
Answer: HCF of 99, 72, 174 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 99, 72, 174 using Euclid's Algorithm?
Answer: For arbitrary numbers 99, 72, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.