Highest Common Factor of 724, 999, 309, 212 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 724, 999, 309, 212 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 724, 999, 309, 212 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 724, 999, 309, 212 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 724, 999, 309, 212 is 1.
HCF(724, 999, 309, 212) = 1
HCF of 724, 999, 309, 212 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 724, 999, 309, 212 is 1.
Highest Common Factor of 724,999,309,212 is 1
Step 1: Since 999 > 724, we apply the division lemma to 999 and 724, to get
999 = 724 x 1 + 275
Step 2: Since the reminder 724 ≠ 0, we apply division lemma to 275 and 724, to get
724 = 275 x 2 + 174
Step 3: We consider the new divisor 275 and the new remainder 174, and apply the division lemma to get
275 = 174 x 1 + 101
We consider the new divisor 174 and the new remainder 101,and apply the division lemma to get
174 = 101 x 1 + 73
We consider the new divisor 101 and the new remainder 73,and apply the division lemma to get
101 = 73 x 1 + 28
We consider the new divisor 73 and the new remainder 28,and apply the division lemma to get
73 = 28 x 2 + 17
We consider the new divisor 28 and the new remainder 17,and apply the division lemma to get
28 = 17 x 1 + 11
We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get
17 = 11 x 1 + 6
We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get
11 = 6 x 1 + 5
We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get
6 = 5 x 1 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 724 and 999 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(28,17) = HCF(73,28) = HCF(101,73) = HCF(174,101) = HCF(275,174) = HCF(724,275) = HCF(999,724) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 309 > 1, we apply the division lemma to 309 and 1, to get
309 = 1 x 309 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 309 is 1
Notice that 1 = HCF(309,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 212 > 1, we apply the division lemma to 212 and 1, to get
212 = 1 x 212 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 212 is 1
Notice that 1 = HCF(212,1) .
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Frequently Asked Questions on HCF of 724, 999, 309, 212 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 724, 999, 309, 212?
Answer: HCF of 724, 999, 309, 212 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 724, 999, 309, 212 using Euclid's Algorithm?
Answer: For arbitrary numbers 724, 999, 309, 212 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.