Highest Common Factor of 460, 169, 853 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 460, 169, 853 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 460, 169, 853 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 460, 169, 853 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 460, 169, 853 is 1.
HCF(460, 169, 853) = 1
HCF of 460, 169, 853 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 460, 169, 853 is 1.
Highest Common Factor of 460,169,853 is 1
Step 1: Since 460 > 169, we apply the division lemma to 460 and 169, to get
460 = 169 x 2 + 122
Step 2: Since the reminder 169 ≠ 0, we apply division lemma to 122 and 169, to get
169 = 122 x 1 + 47
Step 3: We consider the new divisor 122 and the new remainder 47, and apply the division lemma to get
122 = 47 x 2 + 28
We consider the new divisor 47 and the new remainder 28,and apply the division lemma to get
47 = 28 x 1 + 19
We consider the new divisor 28 and the new remainder 19,and apply the division lemma to get
28 = 19 x 1 + 9
We consider the new divisor 19 and the new remainder 9,and apply the division lemma to get
19 = 9 x 2 + 1
We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get
9 = 1 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 460 and 169 is 1
Notice that 1 = HCF(9,1) = HCF(19,9) = HCF(28,19) = HCF(47,28) = HCF(122,47) = HCF(169,122) = HCF(460,169) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 853 > 1, we apply the division lemma to 853 and 1, to get
853 = 1 x 853 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 853 is 1
Notice that 1 = HCF(853,1) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 460, 169, 853 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 460, 169, 853?
Answer: HCF of 460, 169, 853 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 460, 169, 853 using Euclid's Algorithm?
Answer: For arbitrary numbers 460, 169, 853 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.