Highest Common Factor of 549, 900 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 549, 900 i.e. 9 the largest integer that leaves a remainder zero for all numbers.
HCF of 549, 900 is 9 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 549, 900 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 549, 900 is 9.
HCF(549, 900) = 9
HCF of 549, 900 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 549, 900 is 9.
Highest Common Factor of 549,900 is 9
Step 1: Since 900 > 549, we apply the division lemma to 900 and 549, to get
900 = 549 x 1 + 351
Step 2: Since the reminder 549 ≠ 0, we apply division lemma to 351 and 549, to get
549 = 351 x 1 + 198
Step 3: We consider the new divisor 351 and the new remainder 198, and apply the division lemma to get
351 = 198 x 1 + 153
We consider the new divisor 198 and the new remainder 153,and apply the division lemma to get
198 = 153 x 1 + 45
We consider the new divisor 153 and the new remainder 45,and apply the division lemma to get
153 = 45 x 3 + 18
We consider the new divisor 45 and the new remainder 18,and apply the division lemma to get
45 = 18 x 2 + 9
We consider the new divisor 18 and the new remainder 9,and apply the division lemma to get
18 = 9 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 9, the HCF of 549 and 900 is 9
Notice that 9 = HCF(18,9) = HCF(45,18) = HCF(153,45) = HCF(198,153) = HCF(351,198) = HCF(549,351) = HCF(900,549) .
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Frequently Asked Questions on HCF of 549, 900 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 549, 900?
Answer: HCF of 549, 900 is 9 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 549, 900 using Euclid's Algorithm?
Answer: For arbitrary numbers 549, 900 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
