Highest Common Factor of 909, 525, 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 909, 525, 174 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 909, 525, 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 909, 525, 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 909, 525, 174 is 3.
HCF(909, 525, 174) = 3
HCF of 909, 525, 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 909, 525, 174 is 3.
Highest Common Factor of 909,525,174 is 3
Step 1: Since 909 > 525, we apply the division lemma to 909 and 525, to get
909 = 525 x 1 + 384
Step 2: Since the reminder 525 ≠ 0, we apply division lemma to 384 and 525, to get
525 = 384 x 1 + 141
Step 3: We consider the new divisor 384 and the new remainder 141, and apply the division lemma to get
384 = 141 x 2 + 102
We consider the new divisor 141 and the new remainder 102,and apply the division lemma to get
141 = 102 x 1 + 39
We consider the new divisor 102 and the new remainder 39,and apply the division lemma to get
102 = 39 x 2 + 24
We consider the new divisor 39 and the new remainder 24,and apply the division lemma to get
39 = 24 x 1 + 15
We consider the new divisor 24 and the new remainder 15,and apply the division lemma to get
24 = 15 x 1 + 9
We consider the new divisor 15 and the new remainder 9,and apply the division lemma to get
15 = 9 x 1 + 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 909 and 525 is 3
Notice that 3 = HCF(6,3) = HCF(9,6) = HCF(15,9) = HCF(24,15) = HCF(39,24) = HCF(102,39) = HCF(141,102) = HCF(384,141) = HCF(525,384) = HCF(909,525) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 174 > 3, we apply the division lemma to 174 and 3, to get
174 = 3 x 58 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 174 is 3
Notice that 3 = HCF(174,3) .
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Frequently Asked Questions on HCF of 909, 525, 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 909, 525, 174?
Answer: HCF of 909, 525, 174 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 909, 525, 174 using Euclid's Algorithm?
Answer: For arbitrary numbers 909, 525, 174 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.