Highest Common Factor of 542, 399, 21 using Euclid's algorithm
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 542, 399, 21 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 542, 399, 21 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 542, 399, 21 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 542, 399, 21 is 1.
HCF(542, 399, 21) = 1
HCF of 542, 399, 21 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 542, 399, 21 is 1.
Highest Common Factor of 542,399,21 is 1
Step 1: Since 542 > 399, we apply the division lemma to 542 and 399, to get
542 = 399 x 1 + 143
Step 2: Since the reminder 399 ≠ 0, we apply division lemma to 143 and 399, to get
399 = 143 x 2 + 113
Step 3: We consider the new divisor 143 and the new remainder 113, and apply the division lemma to get
143 = 113 x 1 + 30
We consider the new divisor 113 and the new remainder 30,and apply the division lemma to get
113 = 30 x 3 + 23
We consider the new divisor 30 and the new remainder 23,and apply the division lemma to get
30 = 23 x 1 + 7
We consider the new divisor 23 and the new remainder 7,and apply the division lemma to get
23 = 7 x 3 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 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 542 and 399 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(23,7) = HCF(30,23) = HCF(113,30) = HCF(143,113) = HCF(399,143) = HCF(542,399) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 21 > 1, we apply the division lemma to 21 and 1, to get
21 = 1 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21 is 1
Notice that 1 = HCF(21,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 542, 399, 21 using Euclid's Algorithm
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 542, 399, 21?
Answer: HCF of 542, 399, 21 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 542, 399, 21 using Euclid's Algorithm?
Answer: For arbitrary numbers 542, 399, 21 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.