A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
LearnPracticeDownload

 

Factors of 272

Factors of 272 are the list of integers that can be evenly divided into 272. There are overall 10 factors of 272 among which 272 is the biggest factor and its prime factors are 2, 17. The sum of all factors of 272 is 558.

  • All Factors of 272: 1, 2, 4, 8, 16, 17, 34, 68, 136 and 272
  • Negative Factors of 272: -1, -2, -4, -8, -16, -17, -34, -68, -136 and -272
  • Prime Factors of 272: 2, 17
  • Prime Factorization of 272: 24 × 171
  • Sum of Factors of 272: 558
1. What Are the Factors of 272?
2. Factors of 272 by Prime Factorization
3. Factors of 272 in Pairs
4. FAQs on Factors of 272
Factors of 272

What are Factors of 272?

Factors of 272 are pairs of those numbers whose products result in 272. These factors are either prime numbers or composite numbers.

How to Find the Factors of 272?

To find the factors of 272, we will have to find the list of numbers that would divide 272 without leaving any remainder.

  • 272/17 = 16; therefore, 17 is a factor of 272 and 16 is also a factor of 272.
  • 272/34 = 8; therefore, 34 is a factor of 272 and 8 is also a factor of 272.
Similarly we can find other factors. Hence, the factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272.

☛ Also Check:

Factors of 272 by Prime Factorization

The number 272 is composite and therefore it will have prime factors. Now let us learn how to calculate the prime factors of 272. The first step is to divide the number 272 with the smallest prime factor, here it is 2. We keep dividing until it gives a non-zero remainder.
  • 272 ÷ 2 = 136
  • 136 ÷ 2 = 68
  • 68 ÷ 2 = 34
  • 34 ÷ 2 = 17

Further dividing 17 by 2 gives a non-zero remainder. So we stop the process and continue dividing the number 17 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 272 can be written as 24 × 171 where 2, 17 are prime.

 

Factors of 272 in Pairs

Pair factors of 272 are the pairs of numbers that when multiplied give the product 272. The factors of 272 in pairs are:

  • 1 × 272 = (1, 272)
  • 2 × 136 = (2, 136)
  • 4 × 68 = (4, 68)
  • 8 × 34 = (8, 34)
  • 16 × 17 = (16, 17)

Negative pair factors of 272 are:

  • -1 × -272 = (-1, -272)
  • -2 × -136 = (-2, -136)
  • -4 × -68 = (-4, -68)
  • -8 × -34 = (-8, -34)
  • -16 × -17 = (-16, -17)

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

Factors of 272 Solved Examples

  1. Example 1: How many factors are there for 272?

    Solution:

    The factors of 272 are too many, therefore if we can find the prime factorization of 272, then the total number of factors can be calculated using the formula shown below.
    If the prime factorization of the number is ax × by × cz 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 272 = 24 × 171
    Therefore, the total number of factors are (4 + 1) × (1 + 1) = 5 × 2 = 10

  2. Example 2: Find the LCM and Highest Common Factor (HCF) of 272 and 205.

    Solution:

    The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272 and factors of 205 are 1, 5, 41, 205.

    Therefore, the LCM of 272 and 205 is 55760 and Highest Common Factor (HCF) of 272 and 205 is 1.

  3. Example 3: Find if 1, 2, 16, 29, 34 and 68 are factors of 272.

    Solution:

    When we divide 272 by 29 it leaves a remainder. Therefore, the number 29 is not a factor of 272. All numbers except 29 are factors of 272.

  4. Example 4: Find the product of all the prime factors of 272.

    Solution:

    Since, the prime factors of 272 are 2, 17. Therefore, the product of prime factors = 2 × 17 = 34.

Show Solution >

go to slidego to slidego to slidego to slide

 

Ready to see the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything. 

Book a Free Trial Class

 

FAQs on Factors of 272

What are the Factors of 272?

The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272 and its negative factors are -1, -2, -4, -8, -16, -17, -34, -68, -136, -272.

What is the Sum of the Factors of 272?

Sum of all factors of 272 = (24 + 1 - 1)/(2 - 1) × (171 + 1 - 1)/(17 - 1) = 558

What numbers are the Pair Factors of 272?

The pair factors of 272 are (1, 272), (2, 136), (4, 68), (8, 34), (16, 17).

What is the Greatest Common Factor of 272 and 77?

The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272 and the factors of 77 are 1, 7, 11, 77. 272 and 77 have only one common factor which is 1. This implies that 272 and 77 are co-prime.

Hence, the Greatest Common Factor (GCF) of 272 and 77 is 1.

How Many Factors of 272 are also Factors of 165?

Since, the factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272 and factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165. Hence, 272 and 165 have only one common factor which is 1. Therefore, 272 and 165 are co-prime.

Math worksheets and
visual curriculum