Highest Common Factor of 525, 723, 125 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 525, 723, 125 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 525, 723, 125 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 525, 723, 125 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 525, 723, 125 is 1.
HCF(525, 723, 125) = 1
HCF of 525, 723, 125 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 525, 723, 125 is 1.
Highest Common Factor of 525,723,125 is 1
Step 1: Since 723 > 525, we apply the division lemma to 723 and 525, to get
723 = 525 x 1 + 198
Step 2: Since the reminder 525 ≠ 0, we apply division lemma to 198 and 525, to get
525 = 198 x 2 + 129
Step 3: We consider the new divisor 198 and the new remainder 129, and apply the division lemma to get
198 = 129 x 1 + 69
We consider the new divisor 129 and the new remainder 69,and apply the division lemma to get
129 = 69 x 1 + 60
We consider the new divisor 69 and the new remainder 60,and apply the division lemma to get
69 = 60 x 1 + 9
We consider the new divisor 60 and the new remainder 9,and apply the division lemma to get
60 = 9 x 6 + 6
We consider the new divisor 9 and the new remainder 6,and apply the division lemma to get
9 = 6 x 1 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 525 and 723 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(60,9) = HCF(69,60) = HCF(129,69) = HCF(198,129) = HCF(525,198) = HCF(723,525) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 125 > 3, we apply the division lemma to 125 and 3, to get
125 = 3 x 41 + 2
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get
3 = 2 x 1 + 1
Step 3: 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 3 and 125 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(125,3) .
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Frequently Asked Questions on HCF of 525, 723, 125 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 525, 723, 125?
Answer: HCF of 525, 723, 125 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 525, 723, 125 using Euclid's Algorithm?
Answer: For arbitrary numbers 525, 723, 125 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.