Highest Common Factor of 2208, 5732 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 2208, 5732 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 2208, 5732 is 4 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 2208, 5732 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 2208, 5732 is 4.
HCF(2208, 5732) = 4
HCF of 2208, 5732 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2208, 5732 is 4.
Highest Common Factor of 2208,5732 is 4
Step 1: Since 5732 > 2208, we apply the division lemma to 5732 and 2208, to get
5732 = 2208 x 2 + 1316
Step 2: Since the reminder 2208 ≠ 0, we apply division lemma to 1316 and 2208, to get
2208 = 1316 x 1 + 892
Step 3: We consider the new divisor 1316 and the new remainder 892, and apply the division lemma to get
1316 = 892 x 1 + 424
We consider the new divisor 892 and the new remainder 424,and apply the division lemma to get
892 = 424 x 2 + 44
We consider the new divisor 424 and the new remainder 44,and apply the division lemma to get
424 = 44 x 9 + 28
We consider the new divisor 44 and the new remainder 28,and apply the division lemma to get
44 = 28 x 1 + 16
We consider the new divisor 28 and the new remainder 16,and apply the division lemma to get
28 = 16 x 1 + 12
We consider the new divisor 16 and the new remainder 12,and apply the division lemma to get
16 = 12 x 1 + 4
We consider the new divisor 12 and the new remainder 4,and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 2208 and 5732 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(28,16) = HCF(44,28) = HCF(424,44) = HCF(892,424) = HCF(1316,892) = HCF(2208,1316) = HCF(5732,2208) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 2208, 5732 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 2208, 5732?
Answer: HCF of 2208, 5732 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2208, 5732 using Euclid's Algorithm?
Answer: For arbitrary numbers 2208, 5732 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.