Factors of 150

Definition of Factor

A factor of a number is a whole number that can divide the original number without leaving a remainder. In other words, it's a number that fits perfectly into another number. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18. These numbers can divide 18 without leaving a remainder, and they can be multiplied together to get 18. Factors are important in various mathematical operations, such as finding the greatest common divisor, reducing fractions, and solving equations.

Factors of 150

The factors of 150 are numbers that divide 150 without leaving a remainder. These factors are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. Factors are essential in mathematics for simplifying expressions, finding the greatest common divisor, and solving various mathematical problems.

Also Check: Factors of 12

Steps to Calculate the Prime Factors of 150

To find the prime factors of 150, follow these steps:

  1. Divide by the smallest prime number: Start with the smallest prime number that divides 150, which is 2.

    • 150 ÷ 2 = 75

  2. Continue with the next smallest prime number: Since 75 is not divisible by 2, move to the next prime number, which is 3.

    • 75 ÷ 3 = 25

  3. Proceed with the next smallest prime number: Since 25 is not divisible by 3, move to the next prime number, which is 5.

    • 25 ÷ 5 = 5
    • 5 ÷ 5 = 1 (5 is a prime number)

Thus, the prime factorization of 150 is:

  • 2 × 3 × 5 × 5 or 2×3×52

Also Check: Factors of 144

Prime Factorization of 150

Prime factorization breaks down a number into its prime components. To find the prime factors of 150, use the following steps:

  1. Divide by the smallest prime number: Start with 2.

    • 150 ÷ 2 = 75

  2. Divide by the next smallest prime number: Next, use 3.

    • 75 ÷ 3 = 25

  3. Continue with the next smallest prime number: Finally, use 5.

    • 25 ÷ 5 = 5
    • 5 ÷ 5 = 1

The prime factors of 150 are 2, 3, and 5. Expressed in prime factorization:

  • 2×3×52

Prime factorization is useful for many mathematical tasks, including finding the greatest common divisor, reducing fractions, and solving equations.

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Frequently Asked Questions on Factors of 150

No, 150 is not a prime number because it has more than two factors. The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. A prime number should have exactly two factors.

The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

The greatest common factor (GCF) of 100 and 150 is the largest number that divides both 100 and 150 without leaving a remainder. The GCF is 50.

The factors of 360 include 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360. Yes, 150 is a factor of 360.

There are 12 factors of 150.