Highest Common Factor of 578, 940 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, 940 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 940 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, 940 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, 940 is 2.
HCF(578, 940) = 2
HCF of 578, 940 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, 940 is 2.
Highest Common Factor of 578,940 is 2
Step 1: Since 940 > 578, we apply the division lemma to 940 and 578, to get
940 = 578 x 1 + 362
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 362 and 578, to get
578 = 362 x 1 + 216
Step 3: We consider the new divisor 362 and the new remainder 216, and apply the division lemma to get
362 = 216 x 1 + 146
We consider the new divisor 216 and the new remainder 146,and apply the division lemma to get
216 = 146 x 1 + 70
We consider the new divisor 146 and the new remainder 70,and apply the division lemma to get
146 = 70 x 2 + 6
We consider the new divisor 70 and the new remainder 6,and apply the division lemma to get
70 = 6 x 11 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 578 and 940 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(70,6) = HCF(146,70) = HCF(216,146) = HCF(362,216) = HCF(578,362) = HCF(940,578) .
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Frequently Asked Questions on HCF of 578, 940 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, 940?
Answer: HCF of 578, 940 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 940 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 940 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.