Highest Common Factor of 525, 900, 129, 13 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, 900, 129, 13 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 525, 900, 129, 13 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, 900, 129, 13 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, 900, 129, 13 is 1.
HCF(525, 900, 129, 13) = 1
HCF of 525, 900, 129, 13 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, 900, 129, 13 is 1.
Highest Common Factor of 525,900,129,13 is 1
Step 1: Since 900 > 525, we apply the division lemma to 900 and 525, to get
900 = 525 x 1 + 375
Step 2: Since the reminder 525 ≠ 0, we apply division lemma to 375 and 525, to get
525 = 375 x 1 + 150
Step 3: We consider the new divisor 375 and the new remainder 150, and apply the division lemma to get
375 = 150 x 2 + 75
We consider the new divisor 150 and the new remainder 75, and apply the division lemma to get
150 = 75 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 75, the HCF of 525 and 900 is 75
Notice that 75 = HCF(150,75) = HCF(375,150) = HCF(525,375) = HCF(900,525) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 129 > 75, we apply the division lemma to 129 and 75, to get
129 = 75 x 1 + 54
Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 54 and 75, to get
75 = 54 x 1 + 21
Step 3: We consider the new divisor 54 and the new remainder 21, and apply the division lemma to get
54 = 21 x 2 + 12
We consider the new divisor 21 and the new remainder 12,and apply the division lemma to get
21 = 12 x 1 + 9
We consider the new divisor 12 and the new remainder 9,and apply the division lemma to get
12 = 9 x 1 + 3
We consider the new divisor 9 and the new remainder 3,and apply the division lemma 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 75 and 129 is 3
Notice that 3 = HCF(9,3) = HCF(12,9) = HCF(21,12) = HCF(54,21) = HCF(75,54) = HCF(129,75) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 13 > 3, we apply the division lemma to 13 and 3, to get
13 = 3 x 4 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 13 is 1
Notice that 1 = HCF(3,1) = HCF(13,3) .
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Frequently Asked Questions on HCF of 525, 900, 129, 13 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, 900, 129, 13?
Answer: HCF of 525, 900, 129, 13 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 525, 900, 129, 13 using Euclid's Algorithm?
Answer: For arbitrary numbers 525, 900, 129, 13 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.