Highest Common Factor of 645, 473, 889 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 645, 473, 889 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 645, 473, 889 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 645, 473, 889 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 645, 473, 889 is 1.
HCF(645, 473, 889) = 1
HCF of 645, 473, 889 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 645, 473, 889 is 1.
Highest Common Factor of 645,473,889 is 1
Step 1: Since 645 > 473, we apply the division lemma to 645 and 473, to get
645 = 473 x 1 + 172
Step 2: Since the reminder 473 ≠ 0, we apply division lemma to 172 and 473, to get
473 = 172 x 2 + 129
Step 3: We consider the new divisor 172 and the new remainder 129, and apply the division lemma to get
172 = 129 x 1 + 43
We consider the new divisor 129 and the new remainder 43, and apply the division lemma to get
129 = 43 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 43, the HCF of 645 and 473 is 43
Notice that 43 = HCF(129,43) = HCF(172,129) = HCF(473,172) = HCF(645,473) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 889 > 43, we apply the division lemma to 889 and 43, to get
889 = 43 x 20 + 29
Step 2: Since the reminder 43 ≠ 0, we apply division lemma to 29 and 43, to get
43 = 29 x 1 + 14
Step 3: We consider the new divisor 29 and the new remainder 14, and apply the division lemma to get
29 = 14 x 2 + 1
We consider the new divisor 14 and the new remainder 1, and apply the division lemma to get
14 = 1 x 14 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 43 and 889 is 1
Notice that 1 = HCF(14,1) = HCF(29,14) = HCF(43,29) = HCF(889,43) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 645, 473, 889 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 645, 473, 889?
Answer: HCF of 645, 473, 889 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 645, 473, 889 using Euclid's Algorithm?
Answer: For arbitrary numbers 645, 473, 889 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.