Highest Common Factor of 245, 21910 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 245, 21910 i.e. 35 the largest integer that leaves a remainder zero for all numbers.
HCF of 245, 21910 is 35 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 245, 21910 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 245, 21910 is 35.
HCF(245, 21910) = 35
HCF of 245, 21910 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 245, 21910 is 35.
Highest Common Factor of 245,21910 is 35
Step 1: Since 21910 > 245, we apply the division lemma to 21910 and 245, to get
21910 = 245 x 89 + 105
Step 2: Since the reminder 245 ≠ 0, we apply division lemma to 105 and 245, to get
245 = 105 x 2 + 35
Step 3: We consider the new divisor 105 and the new remainder 35, and apply the division lemma to get
105 = 35 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 35, the HCF of 245 and 21910 is 35
Notice that 35 = HCF(105,35) = HCF(245,105) = HCF(21910,245) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 245, 21910 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 245, 21910?
Answer: HCF of 245, 21910 is 35 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 245, 21910 using Euclid's Algorithm?
Answer: For arbitrary numbers 245, 21910 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.