Factors of 280

Mathematically, we know that factors of a number divide that particular number completely. There are a total of 16 factors of 280; hence it is a composite number. There are 3 prime numbers among the 16 factors of 280, which are termed as prime factors of 280. In this lesson, let us learn abuout factors of 280 in detail. We will find how to calculate factors of 280 and factors of 280 in pairs, with solved examples.

• Factors of 280: 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
• Prime Factorization of 280: 2 × 2 × 2 × 5 × 7

Let us explore more about factors of 280 and ways to find them.

Numbers that divide the given number exactly without any remainder are termed as factors . According to the definition of factors, the factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280. So, 280 is a composite number as it has factors other than 1 and itself. There are a total of 16 factors of 280.

We can use different methods like the divisibility test, prime factorization, and the upside-down division method to calculate the factors of 280. In prime factorization, we express 280 as a product of its prime factors, and in the division method, we see which numbers divide 280 exactly without a remainder.

Let us calculate factors of 280 using the follwoing two methods:

• Factors of 280 by division method
• Factors of 280 by prime factorization method

Factors of 280 by Division Method

Let us divide 280 by whole numbers and see which numbers divide 280 exactly without leaving a remainder. 

• 280 ÷ 1 = 280
• 280 ÷ 2 = 140
• 280 ÷ 4 = 70
• 280 ÷ 5 = 56
• 280 ÷ 7 = 40
• 280 ÷ 8 = 35
• 280 ÷ 10 = 28
• 280 ÷ 14 = 20

According to division method we have 0 as a remainder for all the numbers. The divisor and the obtained quotient are the factors of 280. Hence, the factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, and 280. These are the numbers which exactly divide 280 without leaving any remainder.

Prime Factorization of 280

• Here, 280 is an even number.
• Using divisibility rules, find the smallest factor of 280.
• Divide 280 by 2. 280 ÷ 2 = 140
• Here, 2 is the smallest prime factor of 280.
• Now find the prime factors of the obtained quotient.
• 140 is a quotient.
• Divide 140 by 2. 140 ÷ 2 = 70.
• Here 70 is the next quotient.
• Divide 70 by 2 = 70 ÷ 2 = 35
• Divide 35 by 5 = 35 ÷ 5 = 7. Here we can stop the process.
• Prime factorization of 280 is 2 × 2 × 2 × 5 × 7.

Explore factors using illustrations and interactive examples

• Factors of 180: The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
• Factors of 80: The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.
• Factors of 84:  The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
• Factors of 144: The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
• Factors of 75: The factors of 75 are 1, 3, 5, 15, 25, and 75.

Numbers that give 280 when multiplied with each other are called the pair factors of 280.

• 280 = 1 × 280
• 280 = 2 × 140
• 280 = 4 × 70
• 280 = 5 × 56
• 280 = 7 × 40
• 280 = 8 × 35
• 280 = 10 × 28
• 280 = 14 × 20
• Therefore, the factor pairs of 280 are (1, 280), (2, 140), (4, 70), (5, 56), (7, 40), (8, 35), (10, 28), and (14, 20).
• Since the product of two negative numbers is positive, i.e., (-) × (-) = (+)
• Hence, (-1, -280), (-2, -140), (-4, -70), (-5, -56), (-7, -40), (-8, -35), (-10, -28), and (-14, -20) are the negative factor pairs of 280.

• Prove that decimal numbers and fractions cannot be factors of 280.
• Calculate the prime factors of 2800.
• Find all the factors of 280280 using division method.

What are the prime factors of 280?

The prime factors of 280 are 2, 5, and 7.

What is the prime factorization of 280?

Prime factorization of 280 is 2 × 2 × 2 × 5 × 7.

Which is the smallest factor of 280?

Smallest factor of 280 is 1. 2 is the smallest prime factor of 280.

Which is the highest factor of 280?

The highest factor of 280 is 280 itself. 

What are the common factors of 280 and 180?

The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, and 280.
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, and 180.
The common factors of 280 and 180 are 1, 2, 4, 5, 10, and 20.