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 2314, 4221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 2314, 4221 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 2314, 4221 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 2314, 4221 is 1.
HCF(2314, 4221) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2314, 4221 is 1.
Step 1: Since 4221 > 2314, we apply the division lemma to 4221 and 2314, to get
4221 = 2314 x 1 + 1907
Step 2: Since the reminder 2314 ≠ 0, we apply division lemma to 1907 and 2314, to get
2314 = 1907 x 1 + 407
Step 3: We consider the new divisor 1907 and the new remainder 407, and apply the division lemma to get
1907 = 407 x 4 + 279
We consider the new divisor 407 and the new remainder 279,and apply the division lemma to get
407 = 279 x 1 + 128
We consider the new divisor 279 and the new remainder 128,and apply the division lemma to get
279 = 128 x 2 + 23
We consider the new divisor 128 and the new remainder 23,and apply the division lemma to get
128 = 23 x 5 + 13
We consider the new divisor 23 and the new remainder 13,and apply the division lemma to get
23 = 13 x 1 + 10
We consider the new divisor 13 and the new remainder 10,and apply the division lemma to get
13 = 10 x 1 + 3
We consider the new divisor 10 and the new remainder 3,and apply the division lemma to get
10 = 3 x 3 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2314 and 4221 is 1
Notice that 1 = HCF(3,1) = HCF(10,3) = HCF(13,10) = HCF(23,13) = HCF(128,23) = HCF(279,128) = HCF(407,279) = HCF(1907,407) = HCF(2314,1907) = HCF(4221,2314) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 2314, 4221?
Answer: HCF of 2314, 4221 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2314, 4221 using Euclid's Algorithm?
Answer: For arbitrary numbers 2314, 4221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.