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 66, 40, 549 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 66, 40, 549 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 66, 40, 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 66, 40, 549 is 1.
HCF(66, 40, 549) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 66, 40, 549 is 1.
Step 1: Since 66 > 40, we apply the division lemma to 66 and 40, to get
66 = 40 x 1 + 26
Step 2: Since the reminder 40 ≠ 0, we apply division lemma to 26 and 40, to get
40 = 26 x 1 + 14
Step 3: We consider the new divisor 26 and the new remainder 14, and apply the division lemma to get
26 = 14 x 1 + 12
We consider the new divisor 14 and the new remainder 12,and apply the division lemma to get
14 = 12 x 1 + 2
We consider the new divisor 12 and the new remainder 2,and apply the division lemma to get
12 = 2 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 66 and 40 is 2
Notice that 2 = HCF(12,2) = HCF(14,12) = HCF(26,14) = HCF(40,26) = HCF(66,40) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 549 > 2, we apply the division lemma to 549 and 2, to get
549 = 2 x 274 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 549 is 1
Notice that 1 = HCF(2,1) = HCF(549,2) .
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 66, 40, 549?
Answer: HCF of 66, 40, 549 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 66, 40, 549 using Euclid's Algorithm?
Answer: For arbitrary numbers 66, 40, 549 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.