Factors of 49

The factors of 49 are numbers that, when multiplied together, result in 49. These factors include 1, 7, and 49. To find these factors, we can use different methods such as factorization and division. This article explains how to find the factors of 49, including positive and negative pair factors, and provides examples for better understanding.

What are the Factors of 49?

Factors of a number are integers that divide that number exactly without leaving a remainder. For 49, the factors are the numbers that can be multiplied in pairs to give the product 49. The factors of 49 are 1, 7, and 49 because:

  • 1×49=49
  • 7×7=49

Since 49 is a perfect square, it has an odd number of factors.

Also Check: Differential Equations

Pair Factors of 49

The pair factors of 49 can be both positive and negative. Pair factors are pairs of numbers that, when multiplied, result in 49.

Positive Pair Factors:

  • (1,49)(1, 49)(1,49)
  • (7,7)(7, 7)(7,7)

Negative Pair Factors:

  • (−1,−49)(-1, -49)(−1,−49)
  • (−7,−7)(-7, -7)(−7,−7)

Factors of 49 by Division Method

To find the factors of 49 using the division method, we divide 49 by various integers. If the division leaves no remainder, the divisor is a factor of 49.

Division Factor Remainder
49 ÷ 1 49 0
49 ÷ 7 7 0
49 ÷ 49 1 0

As we can see, the numbers 1, 7, and 49 divide 49 exactly, making them the factors of 49.

Prime Factorization of 49

Prime factorization involves breaking down a number into its prime factors. For 49, the prime factors are:

  • 49=7×7
  • In exponent form: 49=72

Also Check: Cubes from 1 to 50

Examples:

  1. Finding the Product of Factors: Rohan wants to know the product of all factors of 49.

    • Factors: 1, 7, 49
    • Product: 1×7×49=343

  2. Calculating the Mean of Factors: Reena needs to find the mean of the factors of 49 for her homework.

    • Factors: 1, 7, 49
    • Mean: (1+7+49)/3=19

Also Check: Cube root table

  1. Common Factors of 45 and 49: To find common factors between 45 and 49:

    • Factors of 49: 1, 7, 49
    • Factors of 45: 1, 3, 5, 9, 15, 45
    • Common factor: 1

  2. Greatest Common Factor (GCF) of 49 and 84:

    • Factors of 49: 1, 7, 49
    • Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
    • GCF: 7
Also Check
Factors of 12 Factors of 144
Factors of 150 Factors of 17
Factors of 20 Factors of 215
Factors of 23 Factors of 25
Factors of 28 Factors of 32
Cumulative Frequency Curved Line
Cylinder Determinant of a Matrix

Related Links

Frequently Asked Questions on Factors of 49

The factors are 1, 7, and 49.

The prime factors are 7 and 7, or 72

The product is 343.

Positive pairs: (1, 49) and (7, 7). Negative pairs: (-1, -49) and (-7, -7).