Highest Common Factor of 309, 900, 537 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 309, 900, 537 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 309, 900, 537 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 309, 900, 537 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 309, 900, 537 is 3.
HCF(309, 900, 537) = 3
HCF of 309, 900, 537 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 309, 900, 537 is 3.
Highest Common Factor of 309,900,537 is 3
Step 1: Since 900 > 309, we apply the division lemma to 900 and 309, to get
900 = 309 x 2 + 282
Step 2: Since the reminder 309 ≠ 0, we apply division lemma to 282 and 309, to get
309 = 282 x 1 + 27
Step 3: We consider the new divisor 282 and the new remainder 27, and apply the division lemma to get
282 = 27 x 10 + 12
We consider the new divisor 27 and the new remainder 12,and apply the division lemma to get
27 = 12 x 2 + 3
We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get
12 = 3 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 309 and 900 is 3
Notice that 3 = HCF(12,3) = HCF(27,12) = HCF(282,27) = HCF(309,282) = HCF(900,309) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 537 > 3, we apply the division lemma to 537 and 3, to get
537 = 3 x 179 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 537 is 3
Notice that 3 = HCF(537,3) .
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Frequently Asked Questions on HCF of 309, 900, 537 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 309, 900, 537?
Answer: HCF of 309, 900, 537 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 309, 900, 537 using Euclid's Algorithm?
Answer: For arbitrary numbers 309, 900, 537 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.