Highest Common Factor of 578, 1048, 1025 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, 1048, 1025 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 578, 1048, 1025 is 1 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, 1048, 1025 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, 1048, 1025 is 1.
HCF(578, 1048, 1025) = 1
HCF of 578, 1048, 1025 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, 1048, 1025 is 1.
Highest Common Factor of 578,1048,1025 is 1
Step 1: Since 1048 > 578, we apply the division lemma to 1048 and 578, to get
1048 = 578 x 1 + 470
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 470 and 578, to get
578 = 470 x 1 + 108
Step 3: We consider the new divisor 470 and the new remainder 108, and apply the division lemma to get
470 = 108 x 4 + 38
We consider the new divisor 108 and the new remainder 38,and apply the division lemma to get
108 = 38 x 2 + 32
We consider the new divisor 38 and the new remainder 32,and apply the division lemma to get
38 = 32 x 1 + 6
We consider the new divisor 32 and the new remainder 6,and apply the division lemma to get
32 = 6 x 5 + 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 578 and 1048 is 2
Notice that 2 = HCF(6,2) = HCF(32,6) = HCF(38,32) = HCF(108,38) = HCF(470,108) = HCF(578,470) = HCF(1048,578) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1025 > 2, we apply the division lemma to 1025 and 2, to get
1025 = 2 x 512 + 1
Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2 and 1025 is 1
Notice that 1 = HCF(2,1) = HCF(1025,2) .
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Frequently Asked Questions on HCF of 578, 1048, 1025 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, 1048, 1025?
Answer: HCF of 578, 1048, 1025 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 578, 1048, 1025 using Euclid's Algorithm?
Answer: For arbitrary numbers 578, 1048, 1025 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.