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 421, 1626, 6001 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 421, 1626, 6001 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 421, 1626, 6001 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 421, 1626, 6001 is 1.
HCF(421, 1626, 6001) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 421, 1626, 6001 is 1.
Step 1: Since 1626 > 421, we apply the division lemma to 1626 and 421, to get
1626 = 421 x 3 + 363
Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 363 and 421, to get
421 = 363 x 1 + 58
Step 3: We consider the new divisor 363 and the new remainder 58, and apply the division lemma to get
363 = 58 x 6 + 15
We consider the new divisor 58 and the new remainder 15,and apply the division lemma to get
58 = 15 x 3 + 13
We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get
15 = 13 x 1 + 2
We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get
13 = 2 x 6 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 421 and 1626 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(58,15) = HCF(363,58) = HCF(421,363) = HCF(1626,421) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 6001 > 1, we apply the division lemma to 6001 and 1, to get
6001 = 1 x 6001 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6001 is 1
Notice that 1 = HCF(6001,1) .
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 421, 1626, 6001?
Answer: HCF of 421, 1626, 6001 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 421, 1626, 6001 using Euclid's Algorithm?
Answer: For arbitrary numbers 421, 1626, 6001 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.