Highest Common Factor of 902, 578 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 902, 578 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 902, 578 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 902, 578 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 902, 578 is 2.
HCF(902, 578) = 2
HCF of 902, 578 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 902, 578 is 2.
Highest Common Factor of 902,578 is 2
Step 1: Since 902 > 578, we apply the division lemma to 902 and 578, to get
902 = 578 x 1 + 324
Step 2: Since the reminder 578 ≠ 0, we apply division lemma to 324 and 578, to get
578 = 324 x 1 + 254
Step 3: We consider the new divisor 324 and the new remainder 254, and apply the division lemma to get
324 = 254 x 1 + 70
We consider the new divisor 254 and the new remainder 70,and apply the division lemma to get
254 = 70 x 3 + 44
We consider the new divisor 70 and the new remainder 44,and apply the division lemma to get
70 = 44 x 1 + 26
We consider the new divisor 44 and the new remainder 26,and apply the division lemma to get
44 = 26 x 1 + 18
We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get
26 = 18 x 1 + 8
We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get
18 = 8 x 2 + 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 902 and 578 is 2
Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(44,26) = HCF(70,44) = HCF(254,70) = HCF(324,254) = HCF(578,324) = HCF(902,578) .
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Frequently Asked Questions on HCF of 902, 578 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 902, 578?
Answer: HCF of 902, 578 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 902, 578 using Euclid's Algorithm?
Answer: For arbitrary numbers 902, 578 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
