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Factors of 1400

Factors of 1400 are integers that can be divided evenly into 1400. There are 24 factors of 1400 of which 1400 itself is the biggest factor and its prime factors are 2, 5, 7 The sum of all factors of 1400 is 3720.

All Factors of 1400: 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700 and 1400
Prime Factors of 1400: 2, 5, 7
Prime Factorization of 1400: 2³ × 5² × 7¹
Sum of Factors of 1400: 3720

1.	What Are the Factors of 1400?
2.	Factors of 1400 by Prime Factorization
3.	Factors of 1400 in Pairs
4.	FAQs on Factors of 1400

What are Factors of 1400?

Factors of 1400 are pairs of those numbers whose products result in 1400. These factors are either prime numbers or composite numbers.

How to Find the Factors of 1400?

To find the factors of 1400, we will have to find the list of numbers that would divide 1400 without leaving any remainder.

1400/10 = 140; therefore, 10 is a factor of 1400 and 140 is also a factor of 1400.
1400/20 = 70; therefore, 20 is a factor of 1400 and 70 is also a factor of 1400.

Similarly we can find other factors. Hence, the factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400.

☛ Also Check:

Factors of 40 - The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
Factors of 7 - The factors of 7 are 1, 7
Factors of 78 - The factors of 78 are 1, 2, 3, 6, 13, 26, 39, 78
Factors of 54 - The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
Factors of 41 - The factors of 41 are 1, 41

Factors of 1400 by Prime Factorization

The number 1400 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 1400. The first step is to divide the number 1400 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.

1400 ÷ 2 = 700
700 ÷ 2 = 350
350 ÷ 2 = 175

Further dividing 175 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 175 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 1400 can be written as 2³ × 5² × 7¹ where 2, 5, 7 are prime.

Factors of 1400 in Pairs

Pair factors of 1400 are the pairs of numbers that when multiplied give the product 1400. The factors of 1400 in pairs are:

1 × 1400 = (1, 1400)
2 × 700 = (2, 700)
4 × 350 = (4, 350)
5 × 280 = (5, 280)
7 × 200 = (7, 200)
8 × 175 = (8, 175)
10 × 140 = (10, 140)
14 × 100 = (14, 100)
20 × 70 = (20, 70)
25 × 56 = (25, 56)
28 × 50 = (28, 50)
35 × 40 = (35, 40)

Negative pair factors of 1400 are:

-1 × -1400 = (-1, -1400)
-2 × -700 = (-2, -700)
-4 × -350 = (-4, -350)
-5 × -280 = (-5, -280)
-7 × -200 = (-7, -200)
-8 × -175 = (-8, -175)
-10 × -140 = (-10, -140)
-14 × -100 = (-14, -100)
-20 × -70 = (-20, -70)
-25 × -56 = (-25, -56)
-28 × -50 = (-28, -50)
-35 × -40 = (-35, -40)

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

Factors of 1400 Solved Examples

Example 1: How many factors are there for 1400?

Solution:

The factors of 1400 are too many, therefore if we can find the prime factorization of 1400, 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 1400 = 2³ × 5² × 7¹
Therefore, the total number of factors are (3 + 1) × (2 + 1) × (1 + 1) = 4 × 3 × 2 = 24
Example 2: Find the Lowest Common Multiple (LCM) and Greatest Common Divisor (GCD) of 1400 and 622.

Solution:

The factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400 and factors of 622 are 1, 2, 311, 622.

Therefore, the Lowest Common Multiple (LCM) of 1400 and 622 is 435400 and Greatest Common Divisor (GCD) of 1400 and 622 is 2.
Example 3: Find if 7, 25, 28, 35, 50, 70, 100 and 136 are factors of 1400.

Solution:

When we divide 1400 by 136 it leaves a remainder. Therefore, the number 136 is not a factor of 1400. All numbers except 136 are factors of 1400.
Example 4: Find the product of all the prime factors of 1400.

Solution:

Since, the prime factors of 1400 are 2, 5, 7. Therefore, the product of prime factors = 2 × 5 × 7 = 70.

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FAQs on Factors of 1400

What are the Factors of 1400?

The factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400 and its negative factors are -1, -2, -4, -5, -7, -8, -10, -14, -20, -25, -28, -35, -40, -50, -56, -70, -100, -140, -175, -200, -280, -350, -700, -1400.

What is the Sum of the Factors of 1400?

Sum of all factors of 1400 = (2^{3 + 1} - 1)/(2 - 1) × (5^{2 + 1} - 1)/(5 - 1) × (7^{1 + 1} - 1)/(7 - 1) = 3720

What are the Prime Factors of 1400?

The prime factors of 1400 are 2, 5, 7.

What is the Greatest Common Factor of 1400 and 642?

The factors of 1400 and 642 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400 and 1, 2, 3, 6, 107, 214, 321, 642 respectively.

Common factors of 1400 and 642 are [1, 2].

Hence, the Greatest Common Factor of 1400 and 642 is 2.

How Many Factors of 1400 are also common to the Factors of 784?

Since, the factors of 1400 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700, 1400 and the factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784.
Hence, [1, 2, 4, 7, 8, 14, 28, 56] are the common factors of 1400 and 784.

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