Highest Common Factor of 2148, 1568 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 2148, 1568 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 2148, 1568 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 2148, 1568 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 2148, 1568 is 4.
HCF(2148, 1568) = 4
HCF of 2148, 1568 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2148, 1568 is 4.
Highest Common Factor of 2148,1568 is 4
Step 1: Since 2148 > 1568, we apply the division lemma to 2148 and 1568, to get
2148 = 1568 x 1 + 580
Step 2: Since the reminder 1568 ≠ 0, we apply division lemma to 580 and 1568, to get
1568 = 580 x 2 + 408
Step 3: We consider the new divisor 580 and the new remainder 408, and apply the division lemma to get
580 = 408 x 1 + 172
We consider the new divisor 408 and the new remainder 172,and apply the division lemma to get
408 = 172 x 2 + 64
We consider the new divisor 172 and the new remainder 64,and apply the division lemma to get
172 = 64 x 2 + 44
We consider the new divisor 64 and the new remainder 44,and apply the division lemma to get
64 = 44 x 1 + 20
We consider the new divisor 44 and the new remainder 20,and apply the division lemma to get
44 = 20 x 2 + 4
We consider the new divisor 20 and the new remainder 4,and apply the division lemma to get
20 = 4 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 2148 and 1568 is 4
Notice that 4 = HCF(20,4) = HCF(44,20) = HCF(64,44) = HCF(172,64) = HCF(408,172) = HCF(580,408) = HCF(1568,580) = HCF(2148,1568) .
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Frequently Asked Questions on HCF of 2148, 1568 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 2148, 1568?
Answer: HCF of 2148, 1568 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2148, 1568 using Euclid's Algorithm?
Answer: For arbitrary numbers 2148, 1568 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.