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 711, 390, 549 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 711, 390, 549 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 711, 390, 549 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 711, 390, 549 is 3.
HCF(711, 390, 549) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 711, 390, 549 is 3.
Step 1: Since 711 > 390, we apply the division lemma to 711 and 390, to get
711 = 390 x 1 + 321
Step 2: Since the reminder 390 ≠ 0, we apply division lemma to 321 and 390, to get
390 = 321 x 1 + 69
Step 3: We consider the new divisor 321 and the new remainder 69, and apply the division lemma to get
321 = 69 x 4 + 45
We consider the new divisor 69 and the new remainder 45,and apply the division lemma to get
69 = 45 x 1 + 24
We consider the new divisor 45 and the new remainder 24,and apply the division lemma to get
45 = 24 x 1 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 711 and 390 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(45,24) = HCF(69,45) = HCF(321,69) = HCF(390,321) = HCF(711,390) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 549 > 3, we apply the division lemma to 549 and 3, to get
549 = 3 x 183 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 549 is 3
Notice that 3 = HCF(549,3) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 711, 390, 549?
Answer: HCF of 711, 390, 549 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 711, 390, 549 using Euclid's Algorithm?
Answer: For arbitrary numbers 711, 390, 549 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.