Highest Common Factor of 235, 21210 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 235, 21210 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 235, 21210 is 5 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 235, 21210 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 235, 21210 is 5.
HCF(235, 21210) = 5
HCF of 235, 21210 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 235, 21210 is 5.
Highest Common Factor of 235,21210 is 5
Step 1: Since 21210 > 235, we apply the division lemma to 21210 and 235, to get
21210 = 235 x 90 + 60
Step 2: Since the reminder 235 ≠ 0, we apply division lemma to 60 and 235, to get
235 = 60 x 3 + 55
Step 3: We consider the new divisor 60 and the new remainder 55, and apply the division lemma to get
60 = 55 x 1 + 5
We consider the new divisor 55 and the new remainder 5, and apply the division lemma to get
55 = 5 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 235 and 21210 is 5
Notice that 5 = HCF(55,5) = HCF(60,55) = HCF(235,60) = HCF(21210,235) .
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Frequently Asked Questions on HCF of 235, 21210 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 235, 21210?
Answer: HCF of 235, 21210 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 235, 21210 using Euclid's Algorithm?
Answer: For arbitrary numbers 235, 21210 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.