Highest Common Factor of 678, 44308 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 678, 44308 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 678, 44308 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 678, 44308 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 678, 44308 is 2.
HCF(678, 44308) = 2
HCF of 678, 44308 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 678, 44308 is 2.
Highest Common Factor of 678,44308 is 2
Step 1: Since 44308 > 678, we apply the division lemma to 44308 and 678, to get
44308 = 678 x 65 + 238
Step 2: Since the reminder 678 ≠ 0, we apply division lemma to 238 and 678, to get
678 = 238 x 2 + 202
Step 3: We consider the new divisor 238 and the new remainder 202, and apply the division lemma to get
238 = 202 x 1 + 36
We consider the new divisor 202 and the new remainder 36,and apply the division lemma to get
202 = 36 x 5 + 22
We consider the new divisor 36 and the new remainder 22,and apply the division lemma to get
36 = 22 x 1 + 14
We consider the new divisor 22 and the new remainder 14,and apply the division lemma to get
22 = 14 x 1 + 8
We consider the new divisor 14 and the new remainder 8,and apply the division lemma to get
14 = 8 x 1 + 6
We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get
8 = 6 x 1 + 2
We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 678 and 44308 is 2
Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(14,8) = HCF(22,14) = HCF(36,22) = HCF(202,36) = HCF(238,202) = HCF(678,238) = HCF(44308,678) .
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Frequently Asked Questions on HCF of 678, 44308 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 678, 44308?
Answer: HCF of 678, 44308 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 678, 44308 using Euclid's Algorithm?
Answer: For arbitrary numbers 678, 44308 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
