Highest Common Factor of 242, 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 242, 378 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 242, 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 242, 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 242, 378 is 2.
HCF(242, 378) = 2
HCF of 242, 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 242, 378 is 2.
Highest Common Factor of 242,378 is 2
Step 1: Since 378 > 242, we apply the division lemma to 378 and 242, to get
378 = 242 x 1 + 136
Step 2: Since the reminder 242 ≠ 0, we apply division lemma to 136 and 242, to get
242 = 136 x 1 + 106
Step 3: We consider the new divisor 136 and the new remainder 106, and apply the division lemma to get
136 = 106 x 1 + 30
We consider the new divisor 106 and the new remainder 30,and apply the division lemma to get
106 = 30 x 3 + 16
We consider the new divisor 30 and the new remainder 16,and apply the division lemma to get
30 = 16 x 1 + 14
We consider the new divisor 16 and the new remainder 14,and apply the division lemma to get
16 = 14 x 1 + 2
We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get
14 = 2 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 242 and 378 is 2
Notice that 2 = HCF(14,2) = HCF(16,14) = HCF(30,16) = HCF(106,30) = HCF(136,106) = HCF(242,136) = HCF(378,242) .
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Frequently Asked Questions on HCF of 242, 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 242, 378?
Answer: HCF of 242, 378 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 242, 378 using Euclid's Algorithm?
Answer: For arbitrary numbers 242, 378 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.