Factors of 429
Factors of 429 are the list of integers that can be evenly divided into 429. There are overall 8 factors of 429 i.e. 1, 3, 11, 13, 33, 39, 143, 429 where 429 is the biggest factor. The Pair Factors of 429 are (1, 429), (3, 143), (11, 39), (13, 33) and its Prime Factors are 3 × 11 × 13.
- All Factors of 429: 1, 3, 11, 13, 33, 39, 143 and 429
- Negative Factors of 429: -1, -3, -11, -13, -33, -39, -143 and -429
- Prime Factors of 429: 3, 11, 13
- Prime Factorization of 429: 31 × 111 × 131
- Sum of Factors of 429: 672
1. | What Are the Factors of 429? |
2. | Factors of 429 by Prime Factorization |
3. | Factors of 429 in Pairs |
4. | FAQs on Factors of 429 |
What are Factors of 429?
Factors of 429 are pairs of those numbers whose products result in 429. These factors are either prime numbers or composite numbers.
How to Find the Factors of 429?
To find the factors of 429, we will have to find the list of numbers that would divide 429 without leaving any remainder.
- 429/39 = 11; therefore, 39 is a factor of 429 and 11 is also a factor of 429.
- 429/13 = 33; therefore, 13 is a factor of 429 and 33 is also a factor of 429.
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- Factors of 50 - The factors of 50 are 1, 2, 5, 10, 25, 50
- Factors of 180 - The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
- Factors of 55 - The factors of 55 are 1, 5, 11, 55
- Factors of 24 - The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 144 - The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
Factors of 429 by Prime Factorization
- 429 ÷ 3 = 143
Further dividing 143 by 3 gives a non-zero remainder. So we stop the process and continue dividing the number 143 by the next smallest prime factor. We stop ultimately if the next prime factor doesn't exist or when we can't divide any further.
So, the prime factorization of 429 can be written as 31 × 111 × 131 where 3, 11, 13 are prime.
Factors of 429 in Pairs
Pair factors of 429 are the pairs of numbers that when multiplied give the product 429. The factors of 429 in pairs are:
- 1 × 429 = (1, 429)
- 3 × 143 = (3, 143)
- 11 × 39 = (11, 39)
- 13 × 33 = (13, 33)
Negative pair factors of 429 are:
- -1 × -429 = (-1, -429)
- -3 × -143 = (-3, -143)
- -11 × -39 = (-11, -39)
- -13 × -33 = (-13, -33)
NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.
Factors of 429 Solved Examples
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Example 1: How many factors are there for 429?
Solution:
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429. Therefore, 429 has 8 factors.
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Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 429 and 226.
Solution:
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429 and factors of 226 are 1, 2, 113, 226.
Therefore, the Lowest Common Multiple (LCM) of 429 and 226 is 96954 and Greatest Common Divisor (GCD) of 429 and 226 is 1. -
Example 3: Find if 3, 11, 33, 39 and 299 are factors of 429.
Solution:
When we divide 429 by 299 it leaves a remainder. Therefore, the number 299 is not a factor of 429. All numbers except 299 are factors of 429.
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Example 4: Find the product of all the prime factors of 429.
Solution:
Since, the prime factors of 429 are 3, 11, 13. Therefore, the product of prime factors = 3 × 11 × 13 = 429.
FAQs on Factors of 429
What are the Factors of 429?
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429 and its negative factors are -1, -3, -11, -13, -33, -39, -143, -429.
What is the Sum of the Factors of 429?
Sum of all factors of 429 = (31 + 1 - 1)/(3 - 1) × (111 + 1 - 1)/(11 - 1) × (131 + 1 - 1)/(13 - 1) = 672
What Numbers are the Prime Factors of 429?
The prime factors of 429 are 3, 11, 13.
What is the Greatest Common Factor of 429 and 172?
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429 and the factors of 172 are 1, 2, 4, 43, 86, 172. 429 and 172 have only one common factor which is 1. This implies that 429 and 172 are co-prime.
Hence, the Greatest Common Factor (GCF) of 429 and 172 is 1.
What are the Common Factors of 429 and 172?
Since, the factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429 and factors of 172 are 1, 2, 4, 43, 86, 172. Hence, 429 and 172 have only one common factor which is 1. Therefore, 429 and 172 are co-prime.
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