Highest Common Factor of 578, 26988 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 578, 26988 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 26988 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 578, 26988 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 578, 26988 is 2.
HCF(578, 26988) = 2
HCF of 578, 26988 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 578, 26988 is 2.
Highest Common Factor of 578,26988 is 2
Step 1: Since 26988 > 578, we apply the division lemma to 26988 and 578, to get
26988 = 578 x 46 + 400
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 400 and 578, to get
578 = 400 x 1 + 178
Step 3: We consider the new divisor 400 and the new remainder 178, and apply the division lemma to get
400 = 178 x 2 + 44
We consider the new divisor 178 and the new remainder 44,and apply the division lemma to get
178 = 44 x 4 + 2
We consider the new divisor 44 and the new remainder 2,and apply the division lemma to get
44 = 2 x 22 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 578 and 26988 is 2
Notice that 2 = HCF(44,2) = HCF(178,44) = HCF(400,178) = HCF(578,400) = HCF(26988,578) .
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Frequently Asked Questions on HCF of 578, 26988 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 578, 26988?
Answer: HCF of 578, 26988 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 26988 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 26988 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.