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, 600, 735, 72 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 549, 600, 735, 72 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 549, 600, 735, 72 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, 600, 735, 72 is 3.
HCF(549, 600, 735, 72) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 549, 600, 735, 72 is 3.
Step 1: Since 600 > 549, we apply the division lemma to 600 and 549, to get
600 = 549 x 1 + 51
Step 2: Since the reminder 549 ≠ 0, we apply division lemma to 51 and 549, to get
549 = 51 x 10 + 39
Step 3: We consider the new divisor 51 and the new remainder 39, and apply the division lemma to get
51 = 39 x 1 + 12
We consider the new divisor 39 and the new remainder 12,and apply the division lemma to get
39 = 12 x 3 + 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 549 and 600 is 3
Notice that 3 = HCF(12,3) = HCF(39,12) = HCF(51,39) = HCF(549,51) = HCF(600,549) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 735 > 3, we apply the division lemma to 735 and 3, to get
735 = 3 x 245 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 735 is 3
Notice that 3 = HCF(735,3) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 72 > 3, we apply the division lemma to 72 and 3, to get
72 = 3 x 24 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 72 is 3
Notice that 3 = HCF(72,3) .
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 549, 600, 735, 72?
Answer: HCF of 549, 600, 735, 72 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 549, 600, 735, 72 using Euclid's Algorithm?
Answer: For arbitrary numbers 549, 600, 735, 72 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.