Factors of 130

130 is a composite number. There are a total of 8 factors of 130. Among the 8 factors, 3 are prime factors. Let us learn abuout factors of 130 in detail. We will find how to calculate factors of 130 and factors of 130 in pairs, with solved examples.

• Factors of 130: 1, 2, 5, 10, 13, 26, 65, and 130
• Prime Factorization of 130: 2 × 5 × 13

Let us explore more about factors of 130 and ways to find them.

Factors of a number are the numbers that divide the given number exactly without any remainder. According to the definition of factors, the factors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130 So,130 is a composite number as it has factors other than 1 and itself.

We can use different methods like divisibility test, prime factorization, and the upside-down division method to calculate the factors of 130. Let us use prime factorization method to find prime factors of 130. In prime factorization, we express 130 as a product of its prime factors, and in the division method, we see which numbers divide 130 exactly without a remainder.

Let us calculate factors of 130 using the following two methods:

• Factors of 130 by upside-down division method
• Factors of 130 by division method

Prime Factorization by Upside-Down Division Method

• With the help of divisibility rules, find out the smallest factor of the given number.
• Here, 130 is an even number.
• Divide 130 by 2 = 130 ÷ 2 = 65. Therefore, 2 is the smallest prime factor of 130.
• Now find the prime factors of the obtained quotient. Here 65 is a quotient.
• Divide 65 by 5 = 65 ÷ 5 = 13. Therefore 5 is the next prime factor of 130.
• Repeat the process till we get a prime number as the quotient.
• The next obtained quotient is 13.
• Divide 13 by 13. Here we can stop the process. Hence, 13 is another prime factor of 130.
• Prime factorization of 130 is 2 × 5 × 13.

Factors of 130 by Division Method

Let us divide 130 by whole numbers and see which number divides 130 exactly without leaving a remainder.

• 130 ÷ 1 = 130
• 130 ÷ 2 = 65
• 130 ÷ 5 = 26
• 130 ÷ 10 = 13
• 130 ÷ 13 = 10
• 130 ÷ 26 = 5
• 130 ÷ 65 = 2
• 130 ÷ 130 = 1

According to division method, we have factors of 130 as 1, 2, 5, 10, 13, 26, 65, and 130. These are the numbers which exactly divide 130 without leaving any remainder.

Explore factors using illustrations and interactive examples

• Factors of 121: The factors of 121 are 1, 11, and 121.
• Factors of 125: The factors of 125 are 1, 5, 25, and 125.
• Factors of 128:  The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.
• Factors of 216: The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216.
• Factors of 65: The factors of 65 are 1, 5, 13, and 65.
• Factors of 132: The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, and 132. 

Numbers that give 130 when multiplied with each other are called the pair factors of 130.

• Therefore, the pair factors of 130 are (1, 130), (65, 2), (26, 5), (13, 10).
• Since the product of two negative numbers is positive, i.e., (-) × (-) = (+)
• Hence, (-1, -130), (-65, -2), (-26, -5), (-13, -10) are also factor pairs of 130.

• Prove that decimal numbers cannot be factors of 130.
• Is it possible to have prime factors of 1300?
• Find all the factors of 1300 using division method

What are the prime factors of 130?

The prime factors of 130 are 2, 5, and 13.

Is 130 a square number?

No, 130 is not a square number. 

Which is the smallest factor of 130?

Smallest factor of 130 is 1. 2 is the smallest prime factor of 130.

Which is the highest factor of 130?

The highest factor of 130 is 130 itself. 

What are the common factors of 130 and 30?

The factors of 130 are 1, 2, 5, 10, 13, 26, 65, and 130
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30
The common factors of 130 and 30 are 1, 2, 5, and 10.