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 574, 889, 43, 241 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 574, 889, 43, 241 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 574, 889, 43, 241 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 574, 889, 43, 241 is 1.
HCF(574, 889, 43, 241) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 574, 889, 43, 241 is 1.
Step 1: Since 889 > 574, we apply the division lemma to 889 and 574, to get
889 = 574 x 1 + 315
Step 2: Since the reminder 574 ≠ 0, we apply division lemma to 315 and 574, to get
574 = 315 x 1 + 259
Step 3: We consider the new divisor 315 and the new remainder 259, and apply the division lemma to get
315 = 259 x 1 + 56
We consider the new divisor 259 and the new remainder 56,and apply the division lemma to get
259 = 56 x 4 + 35
We consider the new divisor 56 and the new remainder 35,and apply the division lemma to get
56 = 35 x 1 + 21
We consider the new divisor 35 and the new remainder 21,and apply the division lemma to get
35 = 21 x 1 + 14
We consider the new divisor 21 and the new remainder 14,and apply the division lemma to get
21 = 14 x 1 + 7
We consider the new divisor 14 and the new remainder 7,and apply the division lemma to get
14 = 7 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 7, the HCF of 574 and 889 is 7
Notice that 7 = HCF(14,7) = HCF(21,14) = HCF(35,21) = HCF(56,35) = HCF(259,56) = HCF(315,259) = HCF(574,315) = HCF(889,574) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 43 > 7, we apply the division lemma to 43 and 7, to get
43 = 7 x 6 + 1
Step 2: Since the reminder 7 ≠ 0, we apply division lemma to 1 and 7, to get
7 = 1 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 7 and 43 is 1
Notice that 1 = HCF(7,1) = HCF(43,7) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 241 > 1, we apply the division lemma to 241 and 1, to get
241 = 1 x 241 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 241 is 1
Notice that 1 = HCF(241,1) .
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 574, 889, 43, 241?
Answer: HCF of 574, 889, 43, 241 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 574, 889, 43, 241 using Euclid's Algorithm?
Answer: For arbitrary numbers 574, 889, 43, 241 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.