Highest Common Factor of 338, 653 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, 653 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 338, 653 is 1 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, 653 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, 653 is 1.
HCF(338, 653) = 1
HCF of 338, 653 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, 653 is 1.
Highest Common Factor of 338,653 is 1
Step 1: Since 653 > 338, we apply the division lemma to 653 and 338, to get
653 = 338 x 1 + 315
Step 2: Since the reminder 338 ≠ 0, we apply division lemma to 315 and 338, to get
338 = 315 x 1 + 23
Step 3: We consider the new divisor 315 and the new remainder 23, and apply the division lemma to get
315 = 23 x 13 + 16
We consider the new divisor 23 and the new remainder 16,and apply the division lemma to get
23 = 16 x 1 + 7
We consider the new divisor 16 and the new remainder 7,and apply the division lemma to get
16 = 7 x 2 + 2
We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get
7 = 2 x 3 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 338 and 653 is 1
Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(16,7) = HCF(23,16) = HCF(315,23) = HCF(338,315) = HCF(653,338) .
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, 653 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, 653?
Answer: HCF of 338, 653 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 338, 653 using Euclid's Algorithm?
Answer: For arbitrary numbers 338, 653 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.