Highest Common Factor of 549, 765, 308 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, 765, 308 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 549, 765, 308 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 549, 765, 308 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, 765, 308 is 1.
HCF(549, 765, 308) = 1
HCF of 549, 765, 308 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, 765, 308 is 1.
Highest Common Factor of 549,765,308 is 1
Step 1: Since 765 > 549, we apply the division lemma to 765 and 549, to get
765 = 549 x 1 + 216
Step 2: Since the reminder 549 ≠ 0, we apply division lemma to 216 and 549, to get
549 = 216 x 2 + 117
Step 3: We consider the new divisor 216 and the new remainder 117, and apply the division lemma to get
216 = 117 x 1 + 99
We consider the new divisor 117 and the new remainder 99,and apply the division lemma to get
117 = 99 x 1 + 18
We consider the new divisor 99 and the new remainder 18,and apply the division lemma to get
99 = 18 x 5 + 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 765 is 9
Notice that 9 = HCF(18,9) = HCF(99,18) = HCF(117,99) = HCF(216,117) = HCF(549,216) = HCF(765,549) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 308 > 9, we apply the division lemma to 308 and 9, to get
308 = 9 x 34 + 2
Step 2: Since the reminder 9 ≠ 0, we apply division lemma to 2 and 9, to get
9 = 2 x 4 + 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 9 and 308 is 1
Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(308,9) .
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Frequently Asked Questions on HCF of 549, 765, 308 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, 765, 308?
Answer: HCF of 549, 765, 308 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 549, 765, 308 using Euclid's Algorithm?
Answer: For arbitrary numbers 549, 765, 308 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.