What are all the factors, the prime factorization, and factor pairs of 49?

Factors are the building blocks of numbers, representing the integers we multiply together to construct other numbers. Focusing on the number 49 as an example, we learn that factors unveil the intrinsic numerical structure and properties within mathematics. Factors of a number like 49 bring to light its divisibility and multiplicativity, essential concepts in math.

The factors of 49 are the numbers which, when multiplied in pairs, yield the product 49. This means all factors of 49 can divide the number without leaving any remainder. Below is a visual representation and a list of the factors of 49:

• 1 × 49 = 49
• 7 × 7 = 49

To find the factors of 49, one can use the division method. This involves dividing 49 by positive integers to determine which result in whole numbers:

• 49 ÷ 1 yields 49, so 1 is a factor.
• 49 ÷ 7 yields 7, showing that 7 is also a factor.

If we divide 49 by any integer other than its factors, the result will not be a whole number. For instance, 49 ÷ 3 equals approximately 16.33, which means 3 is not a factor of 49.

Pair factors of 49 consist of two numbers that, when multiplied together, result in 49. Here is a list of those pair factors, both positive and negative:

Prime factorization involves breaking down a number into its prime factors. The number 49 can be factorized into prime numbers as follows:

• 49 = 7 × 7

Since 7 is a prime number and the only factor that can be multiplied by itself to produce 49, it is the prime factorization of 49.

Key points to keep in mind regarding the factors of 49 include:

• Total factors of 49: 1, 7, and 49.
• Prime factors of 49: 7.
• Pair factors of 49: (1, 49) and (7, 7).
• Sum of all factors of 49: 1 + 7 + 49 = 57.
• 49 is a square number since it is 7 squared (7^2).

• List all the factors of 49.
• Is number 49 a prime or composite number? Explain why.
• What are the pair factors of 49?

• The factors of 49 are: 1, 7, and 49.
• 49 is a composite number because it has factors other than 1 and itself. In this case, 7 is a factor of 49.
• The pair factors of 49 are: (1, 49) and (7, 7).