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 126, 402, 308 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 126, 402, 308 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 126, 402, 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 126, 402, 308 is 2.
HCF(126, 402, 308) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 126, 402, 308 is 2.
Step 1: Since 402 > 126, we apply the division lemma to 402 and 126, to get
402 = 126 x 3 + 24
Step 2: Since the reminder 126 ≠ 0, we apply division lemma to 24 and 126, to get
126 = 24 x 5 + 6
Step 3: We consider the new divisor 24 and the new remainder 6, and apply the division lemma to get
24 = 6 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 126 and 402 is 6
Notice that 6 = HCF(24,6) = HCF(126,24) = HCF(402,126) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 308 > 6, we apply the division lemma to 308 and 6, to get
308 = 6 x 51 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 308 is 2
Notice that 2 = HCF(6,2) = HCF(308,6) .
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 126, 402, 308?
Answer: HCF of 126, 402, 308 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 126, 402, 308 using Euclid's Algorithm?
Answer: For arbitrary numbers 126, 402, 308 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.