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Factors of 1372

Factors of 1372 are numbers that, when multiplied in pairs give the product as 1372. There are 12 factors of 1372 of which 1372 itself is the biggest factor and its prime factors are 2, 7 The sum of all factors of 1372 is 2800.

All Factors of 1372: 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686 and 1372
Prime Factors of 1372: 2, 7
Prime Factorization of 1372: 2² × 7³
Sum of Factors of 1372: 2800

1.	What Are the Factors of 1372?
2.	Factors of 1372 by Prime Factorization
3.	Factors of 1372 in Pairs
4.	FAQs on Factors of 1372

What are Factors of 1372?

Factors of 1372 are pairs of those numbers whose products result in 1372. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1372?

To find the factors of 1372, we will have to find the list of numbers that would divide 1372 without leaving any remainder.

1372/343 = 4; therefore, 343 is a factor of 1372 and 4 is also a factor of 1372.
1372/49 = 28; therefore, 49 is a factor of 1372 and 28 is also a factor of 1372.

Similarly we can find other factors. Hence, the factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372.

☛ Also Check:

Factors of 13 - The factors of 13 are 1, 13
Factors of 51 - The factors of 51 are 1, 3, 17, 51
Factors of 91 - The factors of 91 are 1, 7, 13, 91
Factors of 14 - The factors of 14 are 1, 2, 7, 14
Factors of 7 - The factors of 7 are 1, 7

Factors of 1372 by Prime Factorization

The number 1372 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1372. The first step is to divide the number 1372 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1372 ÷ 2 = 686
686 ÷ 2 = 343

Further dividing 343 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 343 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 1372 can be written as 2² × 7³ where 2, 7 are prime.

Factors of 1372 in Pairs

Pair factors of 1372 are the pairs of numbers that when multiplied give the product 1372. The factors of 1372 in pairs are:

1 × 1372 = (1, 1372)
2 × 686 = (2, 686)
4 × 343 = (4, 343)
7 × 196 = (7, 196)
14 × 98 = (14, 98)
28 × 49 = (28, 49)

Negative pair factors of 1372 are:

-1 × -1372 = (-1, -1372)
-2 × -686 = (-2, -686)
-4 × -343 = (-4, -343)
-7 × -196 = (-7, -196)
-14 × -98 = (-14, -98)
-28 × -49 = (-28, -49)

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

Factors of 1372 Solved Examples

Example 1: How many factors are there for 1372?

Solution:

The factors of 1372 are too many, therefore if we can find the prime factorization of 1372, 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 1372 = 2² × 7³
Therefore, the total number of factors are (2 + 1) × (3 + 1) = 3 × 4 = 12
Example 2: Find the Least Common Multiple and Highest Common Factor (HCF) of 1372 and 541.

Solution:

The factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372 and factors of 541 are 1, 541.

Therefore, the Least Common Multiple of 1372 and 541 is 742252 and Highest Common Factor (HCF) of 1372 and 541 is 1.
Example 3: Find if 1, 2, 4, 7, 98, 196 and 439 are factors of 1372.

Solution:

When we divide 1372 by 439 it leaves a remainder. Therefore, the number 439 is not a factor of 1372. All numbers except 439 are factors of 1372.
Example 4: Find the product of all the prime factors of 1372.

Solution:

Since, the prime factors of 1372 are 2, 7. Therefore, the product of prime factors = 2 × 7 = 14.

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FAQs on Factors of 1372

What are the Factors of 1372?

The factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372 and its negative factors are -1, -2, -4, -7, -14, -28, -49, -98, -196, -343, -686, -1372.

What is the Sum of the Factors of 1372?

Sum of all factors of 1372 = (2^{2 + 1} - 1)/(2 - 1) × (7^{3 + 1} - 1)/(7 - 1) = 2800

What are Prime Factors of 1372?

The prime factors of 1372 are 2, 7.

What is the Greatest Common Factor of 1372 and 61?

The factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372 and the factors of 61 are 1, 61. 1372 and 61 have only one common factor which is 1. This implies that 1372 and 61 are co-prime.

Hence, the Greatest Common Factor (GCF) of 1372 and 61 is 1.

How Many Factors of 167 are also common to the Factors of 1372?

Since, the factors of 1372 are 1, 2, 4, 7, 14, 28, 49, 98, 196, 343, 686, 1372 and factors of 167 are 1, 167. Hence, 1372 and 167 have only one common factor which is 1. Therefore, 1372 and 167 are co-prime.

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