Highest Common Factor of 310, 882 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 310, 882 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 882 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 310, 882 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 310, 882 is 2.
HCF(310, 882) = 2
HCF of 310, 882 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 310, 882 is 2.
Highest Common Factor of 310,882 is 2
Step 1: Since 882 > 310, we apply the division lemma to 882 and 310, to get
882 = 310 x 2 + 262
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 262 and 310, to get
310 = 262 x 1 + 48
Step 3: We consider the new divisor 262 and the new remainder 48, and apply the division lemma to get
262 = 48 x 5 + 22
We consider the new divisor 48 and the new remainder 22,and apply the division lemma to get
48 = 22 x 2 + 4
We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get
22 = 4 x 5 + 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 310 and 882 is 2
Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(48,22) = HCF(262,48) = HCF(310,262) = HCF(882,310) .
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Frequently Asked Questions on HCF of 310, 882 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 310, 882?
Answer: HCF of 310, 882 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 882 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 882 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.