Highest Common Factor of 142, 272 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 142, 272 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 142, 272 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 142, 272 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 142, 272 is 2.
HCF(142, 272) = 2
HCF of 142, 272 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 142, 272 is 2.
Highest Common Factor of 142,272 is 2
Step 1: Since 272 > 142, we apply the division lemma to 272 and 142, to get
272 = 142 x 1 + 130
Step 2: Since the reminder 142 ≠ 0, we apply division lemma to 130 and 142, to get
142 = 130 x 1 + 12
Step 3: We consider the new divisor 130 and the new remainder 12, and apply the division lemma to get
130 = 12 x 10 + 10
We consider the new divisor 12 and the new remainder 10,and apply the division lemma to get
12 = 10 x 1 + 2
We consider the new divisor 10 and the new remainder 2,and apply the division lemma to get
10 = 2 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 142 and 272 is 2
Notice that 2 = HCF(10,2) = HCF(12,10) = HCF(130,12) = HCF(142,130) = HCF(272,142) .
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Frequently Asked Questions on HCF of 142, 272 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 142, 272?
Answer: HCF of 142, 272 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 142, 272 using Euclid's Algorithm?
Answer: For arbitrary numbers 142, 272 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.