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 420, 432, 308 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 420, 432, 308 is 4 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 420, 432, 308 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 420, 432, 308 is 4.
HCF(420, 432, 308) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 420, 432, 308 is 4.
Step 1: Since 432 > 420, we apply the division lemma to 432 and 420, to get
432 = 420 x 1 + 12
Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 12 and 420, to get
420 = 12 x 35 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 12, the HCF of 420 and 432 is 12
Notice that 12 = HCF(420,12) = HCF(432,420) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 308 > 12, we apply the division lemma to 308 and 12, to get
308 = 12 x 25 + 8
Step 2: Since the reminder 12 ≠ 0, we apply division lemma to 8 and 12, to get
12 = 8 x 1 + 4
Step 3: We consider the new divisor 8 and the new remainder 4, and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 12 and 308 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(308,12) .
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 420, 432, 308?
Answer: HCF of 420, 432, 308 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 420, 432, 308 using Euclid's Algorithm?
Answer: For arbitrary numbers 420, 432, 308 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.