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 180, 452, 462 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 180, 452, 462 is 2 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 180, 452, 462 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 180, 452, 462 is 2.
HCF(180, 452, 462) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 180, 452, 462 is 2.
Step 1: Since 452 > 180, we apply the division lemma to 452 and 180, to get
452 = 180 x 2 + 92
Step 2: Since the reminder 180 ≠ 0, we apply division lemma to 92 and 180, to get
180 = 92 x 1 + 88
Step 3: We consider the new divisor 92 and the new remainder 88, and apply the division lemma to get
92 = 88 x 1 + 4
We consider the new divisor 88 and the new remainder 4, and apply the division lemma to get
88 = 4 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 180 and 452 is 4
Notice that 4 = HCF(88,4) = HCF(92,88) = HCF(180,92) = HCF(452,180) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 462 > 4, we apply the division lemma to 462 and 4, to get
462 = 4 x 115 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 462 is 2
Notice that 2 = HCF(4,2) = HCF(462,4) .
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 180, 452, 462?
Answer: HCF of 180, 452, 462 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 180, 452, 462 using Euclid's Algorithm?
Answer: For arbitrary numbers 180, 452, 462 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.