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 414, 3828, 1277 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 414, 3828, 1277 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 414, 3828, 1277 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 414, 3828, 1277 is 1.
HCF(414, 3828, 1277) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 414, 3828, 1277 is 1.
Step 1: Since 3828 > 414, we apply the division lemma to 3828 and 414, to get
3828 = 414 x 9 + 102
Step 2: Since the reminder 414 ≠ 0, we apply division lemma to 102 and 414, to get
414 = 102 x 4 + 6
Step 3: We consider the new divisor 102 and the new remainder 6, and apply the division lemma to get
102 = 6 x 17 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 414 and 3828 is 6
Notice that 6 = HCF(102,6) = HCF(414,102) = HCF(3828,414) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1277 > 6, we apply the division lemma to 1277 and 6, to get
1277 = 6 x 212 + 5
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 5 and 6, to get
6 = 5 x 1 + 1
Step 3: We consider the new divisor 5 and the new remainder 1, and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 6 and 1277 is 1
Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(1277,6) .
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 414, 3828, 1277?
Answer: HCF of 414, 3828, 1277 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 414, 3828, 1277 using Euclid's Algorithm?
Answer: For arbitrary numbers 414, 3828, 1277 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.