Highest Common Factor of 405, 142 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 405, 142 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 405, 142 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 405, 142 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 405, 142 is 1.
HCF(405, 142) = 1
HCF of 405, 142 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 405, 142 is 1.
Highest Common Factor of 405,142 is 1
Step 1: Since 405 > 142, we apply the division lemma to 405 and 142, to get
405 = 142 x 2 + 121
Step 2: Since the reminder 142 ≠ 0, we apply division lemma to 121 and 142, to get
142 = 121 x 1 + 21
Step 3: We consider the new divisor 121 and the new remainder 21, and apply the division lemma to get
121 = 21 x 5 + 16
We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get
21 = 16 x 1 + 5
We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get
16 = 5 x 3 + 1
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 405 and 142 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(121,21) = HCF(142,121) = HCF(405,142) .
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Frequently Asked Questions on HCF of 405, 142 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 405, 142?
Answer: HCF of 405, 142 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 405, 142 using Euclid's Algorithm?
Answer: For arbitrary numbers 405, 142 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.