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 2128, 595 i.e. 7 the largest integer that leaves a remainder zero for all numbers.
HCF of 2128, 595 is 7 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 2128, 595 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 2128, 595 is 7.
HCF(2128, 595) = 7
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 2128, 595 is 7.
Step 1: Since 2128 > 595, we apply the division lemma to 2128 and 595, to get
2128 = 595 x 3 + 343
Step 2: Since the reminder 595 ≠ 0, we apply division lemma to 343 and 595, to get
595 = 343 x 1 + 252
Step 3: We consider the new divisor 343 and the new remainder 252, and apply the division lemma to get
343 = 252 x 1 + 91
We consider the new divisor 252 and the new remainder 91,and apply the division lemma to get
252 = 91 x 2 + 70
We consider the new divisor 91 and the new remainder 70,and apply the division lemma to get
91 = 70 x 1 + 21
We consider the new divisor 70 and the new remainder 21,and apply the division lemma to get
70 = 21 x 3 + 7
We consider the new divisor 21 and the new remainder 7,and apply the division lemma to get
21 = 7 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 2128 and 595 is 7
Notice that 7 = HCF(21,7) = HCF(70,21) = HCF(91,70) = HCF(252,91) = HCF(343,252) = HCF(595,343) = HCF(2128,595) .
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 2128, 595?
Answer: HCF of 2128, 595 is 7 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 2128, 595 using Euclid's Algorithm?
Answer: For arbitrary numbers 2128, 595 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.