Highest Common Factor of 310, 522 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, 522 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 310, 522 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, 522 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, 522 is 2.
HCF(310, 522) = 2
HCF of 310, 522 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, 522 is 2.
Highest Common Factor of 310,522 is 2
Step 1: Since 522 > 310, we apply the division lemma to 522 and 310, to get
522 = 310 x 1 + 212
Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 212 and 310, to get
310 = 212 x 1 + 98
Step 3: We consider the new divisor 212 and the new remainder 98, and apply the division lemma to get
212 = 98 x 2 + 16
We consider the new divisor 98 and the new remainder 16,and apply the division lemma to get
98 = 16 x 6 + 2
We consider the new divisor 16 and the new remainder 2,and apply the division lemma to get
16 = 2 x 8 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 310 and 522 is 2
Notice that 2 = HCF(16,2) = HCF(98,16) = HCF(212,98) = HCF(310,212) = HCF(522,310) .
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Frequently Asked Questions on HCF of 310, 522 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, 522?
Answer: HCF of 310, 522 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 310, 522 using Euclid's Algorithm?
Answer: For arbitrary numbers 310, 522 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.