Highest Common Factor of 902, 314 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, 314 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 902, 314 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, 314 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, 314 is 2.
HCF(902, 314) = 2
HCF of 902, 314 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, 314 is 2.
Highest Common Factor of 902,314 is 2
Step 1: Since 902 > 314, we apply the division lemma to 902 and 314, to get
902 = 314 x 2 + 274
Step 2: Since the reminder 314 ≠ 0, we apply division lemma to 274 and 314, to get
314 = 274 x 1 + 40
Step 3: We consider the new divisor 274 and the new remainder 40, and apply the division lemma to get
274 = 40 x 6 + 34
We consider the new divisor 40 and the new remainder 34,and apply the division lemma to get
40 = 34 x 1 + 6
We consider the new divisor 34 and the new remainder 6,and apply the division lemma to get
34 = 6 x 5 + 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 902 and 314 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(34,6) = HCF(40,34) = HCF(274,40) = HCF(314,274) = HCF(902,314) .
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Frequently Asked Questions on HCF of 902, 314 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, 314?
Answer: HCF of 902, 314 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 902, 314 using Euclid's Algorithm?
Answer: For arbitrary numbers 902, 314 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.