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Factors of 1420

Factors of 1420 are numbers that, when multiplied in pairs give the product as 1420. There are overall 12 factors of 1420 among which 1420 is the biggest factor and 2, 5, 71 are its prime factors. The Prime Factorization of 1420 is 2² × 5¹ × 71¹.

All Factors of 1420: 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710 and 1420
Prime Factors of 1420: 2, 5, 71
Prime Factorization of 1420: 2² × 5¹ × 71¹
Sum of Factors of 1420: 3024

1.	What Are the Factors of 1420?
2.	Factors of 1420 by Prime Factorization
3.	Factors of 1420 in Pairs
4.	FAQs on Factors of 1420

What are Factors of 1420?

Factors of 1420 are pairs of those numbers whose products result in 1420. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1420?

To find the factors of 1420, we will have to find the list of numbers that would divide 1420 without leaving any remainder.

1420/5 = 284; therefore, 5 is a factor of 1420 and 284 is also a factor of 1420.
1420/710 = 2; therefore, 710 is a factor of 1420 and 2 is also a factor of 1420.

Similarly we can find other factors. Hence, the factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420.

☛ Also Check:

Factors of 16 - The factors of 16 are 1, 2, 4, 8, 16
Factors of 22 - The factors of 22 are 1, 2, 11, 22
Factors of 45 - The factors of 45 are 1, 3, 5, 9, 15, 45
Factors of 34 - The factors of 34 are 1, 2, 17, 34
Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40

Factors of 1420 by Prime Factorization

The number 1420 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1420. The first step is to divide the number 1420 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1420 ÷ 2 = 710
710 ÷ 2 = 355

Further dividing 355 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 355 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 1420 can be written as 2² × 5¹ × 71¹ where 2, 5, 71 are prime.

Factors of 1420 in Pairs

Pair factors of 1420 are the pairs of numbers that when multiplied give the product 1420. The factors of 1420 in pairs are:

1 × 1420 = (1, 1420)
2 × 710 = (2, 710)
4 × 355 = (4, 355)
5 × 284 = (5, 284)
10 × 142 = (10, 142)
20 × 71 = (20, 71)

Negative pair factors of 1420 are:

-1 × -1420 = (-1, -1420)
-2 × -710 = (-2, -710)
-4 × -355 = (-4, -355)
-5 × -284 = (-5, -284)
-10 × -142 = (-10, -142)
-20 × -71 = (-20, -71)

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

Factors of 1420 Solved Examples

Example 1: How many factors are there for 1420?

Solution:

The factors of 1420 are too many, therefore if we can find the prime factorization of 1420, 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 1420 = 2² × 5¹ × 71¹
Therefore, the total number of factors are (2 + 1) × (1 + 1) × (1 + 1) = 3 × 2 × 2 = 12
Example 2: Find the Least Common Multiple (LCM) and Highest Common Factor (HCF) of 1420 and 780.

Solution:

The factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420 and factors of 780 are 1, 2, 3, 4, 5, 6, 10, 12, 13, 15, 20, 26, 30, 39, 52, 60, 65, 78, 130, 156, 195, 260, 390, 780.

Therefore, the Least Common Multiple (LCM) of 1420 and 780 is 55380 and Highest Common Factor (HCF) of 1420 and 780 is 20.
Example 3: Find if 5, 10, 20, 71, 142, 344 and 1420 are factors of 1420.

Solution:

When we divide 1420 by 344 it leaves a remainder. Therefore, the number 344 is not a factor of 1420. All numbers except 344 are factors of 1420.
Example 4: Find the product of all the prime factors of 1420.

Solution:

Since, the prime factors of 1420 are 2, 5, 71. Therefore, the product of prime factors = 2 × 5 × 71 = 710.

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FAQs on Factors of 1420

What are the Factors of 1420?

The factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420 and its negative factors are -1, -2, -4, -5, -10, -20, -71, -142, -284, -355, -710, -1420.

What is the Sum of all Factors of 1420?

Sum of all factors of 1420 = (2^{2 + 1} - 1)/(2 - 1) × (5^{1 + 1} - 1)/(5 - 1) × (71^{1 + 1} - 1)/(71 - 1) = 3024

What are Prime Factors of 1420?

The prime factors of 1420 are 2, 5, 71.

What is the Greatest Common Factor of 1420 and 779?

The factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420 and the factors of 779 are 1, 19, 41, 779. 1420 and 779 have only one common factor which is 1. This implies that 1420 and 779 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1420 and 779 is 1.

How Many Factors of 933 are also common to the Factors of 1420?

Since, the factors of 1420 are 1, 2, 4, 5, 10, 20, 71, 142, 284, 355, 710, 1420 and factors of 933 are 1, 3, 311, 933. Hence, 1420 and 933 have only one common factor which is 1. Therefore, 1420 and 933 are co-prime.

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