Highest Common Factor of 142, 378 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, 378 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 142, 378 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, 378 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, 378 is 2.
HCF(142, 378) = 2
HCF of 142, 378 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, 378 is 2.
Highest Common Factor of 142,378 is 2
Step 1: Since 378 > 142, we apply the division lemma to 378 and 142, to get
378 = 142 x 2 + 94
Step 2: Since the reminder 142 ≠ 0, we apply division lemma to 94 and 142, to get
142 = 94 x 1 + 48
Step 3: We consider the new divisor 94 and the new remainder 48, and apply the division lemma to get
94 = 48 x 1 + 46
We consider the new divisor 48 and the new remainder 46,and apply the division lemma to get
48 = 46 x 1 + 2
We consider the new divisor 46 and the new remainder 2,and apply the division lemma to get
46 = 2 x 23 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 142 and 378 is 2
Notice that 2 = HCF(46,2) = HCF(48,46) = HCF(94,48) = HCF(142,94) = HCF(378,142) .
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Frequently Asked Questions on HCF of 142, 378 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, 378?
Answer: HCF of 142, 378 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 142, 378 using Euclid's Algorithm?
Answer: For arbitrary numbers 142, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.