Highest Common Factor of 431, 1046 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 431, 1046 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 431, 1046 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 431, 1046 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 431, 1046 is 1.
HCF(431, 1046) = 1
HCF of 431, 1046 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 431, 1046 is 1.
Highest Common Factor of 431,1046 is 1
Step 1: Since 1046 > 431, we apply the division lemma to 1046 and 431, to get
1046 = 431 x 2 + 184
Step 2: Since the reminder 431 ≠ 0, we apply division lemma to 184 and 431, to get
431 = 184 x 2 + 63
Step 3: We consider the new divisor 184 and the new remainder 63, and apply the division lemma to get
184 = 63 x 2 + 58
We consider the new divisor 63 and the new remainder 58,and apply the division lemma to get
63 = 58 x 1 + 5
We consider the new divisor 58 and the new remainder 5,and apply the division lemma to get
58 = 5 x 11 + 3
We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get
5 = 3 x 1 + 2
We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get
3 = 2 x 1 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 431 and 1046 is 1
Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(58,5) = HCF(63,58) = HCF(184,63) = HCF(431,184) = HCF(1046,431) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 431, 1046 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 431, 1046?
Answer: HCF of 431, 1046 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 431, 1046 using Euclid's Algorithm?
Answer: For arbitrary numbers 431, 1046 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.