Highest Common Factor of 378, 5944 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 378, 5944 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 378, 5944 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 378, 5944 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 378, 5944 is 2.
HCF(378, 5944) = 2
HCF of 378, 5944 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 378, 5944 is 2.
Highest Common Factor of 378,5944 is 2
Step 1: Since 5944 > 378, we apply the division lemma to 5944 and 378, to get
5944 = 378 x 15 + 274
Step 2: Since the reminder 378 ≠ 0, we apply division lemma to 274 and 378, to get
378 = 274 x 1 + 104
Step 3: We consider the new divisor 274 and the new remainder 104, and apply the division lemma to get
274 = 104 x 2 + 66
We consider the new divisor 104 and the new remainder 66,and apply the division lemma to get
104 = 66 x 1 + 38
We consider the new divisor 66 and the new remainder 38,and apply the division lemma to get
66 = 38 x 1 + 28
We consider the new divisor 38 and the new remainder 28,and apply the division lemma to get
38 = 28 x 1 + 10
We consider the new divisor 28 and the new remainder 10,and apply the division lemma to get
28 = 10 x 2 + 8
We consider the new divisor 10 and the new remainder 8,and apply the division lemma to get
10 = 8 x 1 + 2
We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get
8 = 2 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 378 and 5944 is 2
Notice that 2 = HCF(8,2) = HCF(10,8) = HCF(28,10) = HCF(38,28) = HCF(66,38) = HCF(104,66) = HCF(274,104) = HCF(378,274) = HCF(5944,378) .
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Frequently Asked Questions on HCF of 378, 5944 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 378, 5944?
Answer: HCF of 378, 5944 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 378, 5944 using Euclid's Algorithm?
Answer: For arbitrary numbers 378, 5944 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.