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 432, 180, 546 i.e. 6 the largest integer that leaves a remainder zero for all numbers.
HCF of 432, 180, 546 is 6 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 432, 180, 546 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 432, 180, 546 is 6.
HCF(432, 180, 546) = 6
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 432, 180, 546 is 6.
Step 1: Since 432 > 180, we apply the division lemma to 432 and 180, to get
432 = 180 x 2 + 72
Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 72 and 180, to get
180 = 72 x 2 + 36
Step 3: We consider the new divisor 72 and the new remainder 36, and apply the division lemma to get
72 = 36 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 36, the HCF of 432 and 180 is 36
Notice that 36 = HCF(72,36) = HCF(180,72) = HCF(432,180) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 546 > 36, we apply the division lemma to 546 and 36, to get
546 = 36 x 15 + 6
Step 2: Since the reminder 36 ≠ 0, we apply division lemma to 6 and 36, to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 36 and 546 is 6
Notice that 6 = HCF(36,6) = HCF(546,36) .
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 432, 180, 546?
Answer: HCF of 432, 180, 546 is 6 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 432, 180, 546 using Euclid's Algorithm?
Answer: For arbitrary numbers 432, 180, 546 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.