Highest Common Factor of 148, 723, 129, 204 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 148, 723, 129, 204 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 148, 723, 129, 204 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 148, 723, 129, 204 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 148, 723, 129, 204 is 1.
HCF(148, 723, 129, 204) = 1
HCF of 148, 723, 129, 204 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 148, 723, 129, 204 is 1.
Highest Common Factor of 148,723,129,204 is 1
Step 1: Since 723 > 148, we apply the division lemma to 723 and 148, to get
723 = 148 x 4 + 131
Step 2: Since the reminder 148 ≠ 0, we apply division lemma to 131 and 148, to get
148 = 131 x 1 + 17
Step 3: We consider the new divisor 131 and the new remainder 17, and apply the division lemma to get
131 = 17 x 7 + 12
We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get
17 = 12 x 1 + 5
We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get
12 = 5 x 2 + 2
We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get
5 = 2 x 2 + 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 148 and 723 is 1
Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(131,17) = HCF(148,131) = HCF(723,148) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 129 > 1, we apply the division lemma to 129 and 1, to get
129 = 1 x 129 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 129 is 1
Notice that 1 = HCF(129,1) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 204 > 1, we apply the division lemma to 204 and 1, to get
204 = 1 x 204 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 204 is 1
Notice that 1 = HCF(204,1) .
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Frequently Asked Questions on HCF of 148, 723, 129, 204 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 148, 723, 129, 204?
Answer: HCF of 148, 723, 129, 204 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 148, 723, 129, 204 using Euclid's Algorithm?
Answer: For arbitrary numbers 148, 723, 129, 204 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.