A day full of math games & activities. Find one near you.

Factors of 1430

Factors of 1430 are numbers that, when multiplied in pairs give the product as 1430. It has total 16 factors of which 1430 is the biggest factor and the prime factors of 1430 are 2, 5, 11, 13. The Prime Factorization of 1430 is 2¹ × 5¹ × 11¹ × 13¹.

All Factors of 1430: 1, 2, 5, 10, 11, 13, 22, 26, 55, 65, 110, 130, 143, 286, 715 and 1430
Prime Factors of 1430: 2, 5, 11, 13
Prime Factorization of 1430: 2¹ × 5¹ × 11¹ × 13¹
Sum of Factors of 1430: 3024

1.	What Are the Factors of 1430?
2.	Factors of 1430 by Prime Factorization
3.	Factors of 1430 in Pairs
4.	FAQs on Factors of 1430

What are Factors of 1430?

Factors of 1430 are pairs of those numbers whose products result in 1430. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1430?

To find the factors of 1430, we will have to find the list of numbers that would divide 1430 without leaving any remainder.

1430/22 = 65; therefore, 22 is a factor of 1430 and 65 is also a factor of 1430.
1430/2 = 715; therefore, 2 is a factor of 1430 and 715 is also a factor of 1430.

Similarly we can find other factors. Hence, the factors of 1430 are 1, 2, 5, 10, 11, 13, 22, 26, 55, 65, 110, 130, 143, 286, 715, 1430.

☛ Also Check:

Factors of 7 - The factors of 7 are 1, 7
Factors of 32 - The factors of 32 are 1, 2, 4, 8, 16, 32
Factors of 29 - The factors of 29 are 1, 29
Factors of 84 - The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Factors of 70 - The factors of 70 are 1, 2, 5, 7, 10, 14, 35, 70

Factors of 1430 by Prime Factorization

The number 1430 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1430. The first step is to divide the number 1430 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1430 ÷ 2 = 715

Further dividing 715 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 715 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 1430 can be written as 2¹ × 5¹ × 11¹ × 13¹ where 2, 5, 11, 13 are prime.

Factors of 1430 in Pairs

Pair factors of 1430 are the pairs of numbers that when multiplied give the product 1430. The factors of 1430 in pairs are:

1 × 1430 = (1, 1430)
2 × 715 = (2, 715)
5 × 286 = (5, 286)
10 × 143 = (10, 143)
11 × 130 = (11, 130)
13 × 110 = (13, 110)
22 × 65 = (22, 65)
26 × 55 = (26, 55)

Negative pair factors of 1430 are:

-1 × -1430 = (-1, -1430)
-2 × -715 = (-2, -715)
-5 × -286 = (-5, -286)
-10 × -143 = (-10, -143)
-11 × -130 = (-11, -130)
-13 × -110 = (-13, -110)
-22 × -65 = (-22, -65)
-26 × -55 = (-26, -55)

NOTE: If (a, b) is a pair factor of a number then (b, a) is also a pair factor of that number.

Factors of 1430 Solved Examples

Example 1: How many factors are there for 1430?

Solution:

The factors of 1430 are too many, therefore if we can find the prime factorization of 1430, then the total number of factors can be calculated using the formula shown below.
If the prime factorization of the number is a^x × b^y × c^z where a, b, c are prime, then the total number of factors can be given by (x + 1)(y + 1)(z + 1).

Prime Factorization of 1430 = 2¹ × 5¹ × 11¹ × 13¹
Therefore, the total number of factors are (1 + 1) × (1 + 1) × (1 + 1) × (1 + 1) = 2 × 2 × 2 × 2 = 16
Example 2: Find the LCM and Highest Common Factor (HCF) of 1430 and 415.

Solution:

The factors of 1430 are 1, 2, 5, 10, 11, 13, 22, 26, 55, 65, 110, 130, 143, 286, 715, 1430 and factors of 415 are 1, 5, 83, 415.

Therefore, the LCM of 1430 and 415 is 118690 and Highest Common Factor (HCF) of 1430 and 415 is 5.
Example 3: Find if 1, 5, 10, 13, 22, 76, 130 and 1430 are factors of 1430.

Solution:

When we divide 1430 by 76 it leaves a remainder. Therefore, the number 76 is not a factor of 1430. All numbers except 76 are factors of 1430.
Example 4: Find the product of all the prime factors of 1430.

Solution:

Since, the prime factors of 1430 are 2, 5, 11, 13. Therefore, the product of prime factors = 2 × 5 × 11 × 13 = 1430.

go to slide go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

go to slide go to slide go to slide go to slide go to slide

FAQs on Factors of 1430

What are the Factors of 1430?

The factors of 1430 are 1, 2, 5, 10, 11, 13, 22, 26, 55, 65, 110, 130, 143, 286, 715, 1430 and its negative factors are -1, -2, -5, -10, -11, -13, -22, -26, -55, -65, -110, -130, -143, -286, -715, -1430.

What is the Sum of all Factors of 1430?

Sum of all factors of 1430 = (2^{1 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (11^{1 + 1} - 1)/(11 - 1) × (13^{1 + 1} - 1)/(13 - 1) = 3024

What Numbers are the Prime Factors of 1430?

The prime factors of 1430 are 2, 5, 11, 13.

What is the Greatest Common Factor of 1430 and 853?

The factors of 1430 are 1, 2, 5, 10, 11, 13, 22, 26, 55, 65, 110, 130, 143, 286, 715, 1430 and the factors of 853 are 1, 853. 1430 and 853 have only one common factor which is 1. This implies that 1430 and 853 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1430 and 853 is 1.

How Many Factors of 1430 are also Factors of 131?

Since, the factors of 1430 are 1, 2, 5, 10, 11, 13, 22, 26, 55, 65, 110, 130, 143, 286, 715, 1430 and factors of 131 are 1, 131. Hence, 1430 and 131 have only one common factor which is 1. Therefore, 1430 and 131 are co-prime.

Math worksheets and
visual curriculum