Highest Common Factor of 338, 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 338, 522 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 338, 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 338, 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 338, 522 is 2.
HCF(338, 522) = 2
HCF of 338, 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 338, 522 is 2.
Highest Common Factor of 338,522 is 2
Step 1: Since 522 > 338, we apply the division lemma to 522 and 338, to get
522 = 338 x 1 + 184
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 184 and 338, to get
338 = 184 x 1 + 154
Step 3: We consider the new divisor 184 and the new remainder 154, and apply the division lemma to get
184 = 154 x 1 + 30
We consider the new divisor 154 and the new remainder 30,and apply the division lemma to get
154 = 30 x 5 + 4
We consider the new divisor 30 and the new remainder 4,and apply the division lemma to get
30 = 4 x 7 + 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 338 and 522 is 2
Notice that 2 = HCF(4,2) = HCF(30,4) = HCF(154,30) = HCF(184,154) = HCF(338,184) = HCF(522,338) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 338, 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 338, 522?
Answer: HCF of 338, 522 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 338, 522 using Euclid's Algorithm?
Answer: For arbitrary numbers 338, 522 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
