Factors of 192

Factors of 192 are the list of positive and negative whole numbers that can be divided evenly into 192. Do you know that the number 192 is called a Harshad number? This is because the number is exactly divisible by the sum of its digits.

In this mini-lesson, we will explore the world of factors of 192 in math. You will get to learn about the way to calculate the factors of 192 by using the factor tree and the prime factorization, factor pairs of 192, and other interesting facts around the topic. You can try your hand at solving a few interesting practice questions at the end of the page.

• Factors of 192: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192
• Negative factors of 192: -1, -2, -3, -4, -6, -8, -12, -16, -24, -32, -48, -64, -96, and -192
• Prime Factorization of 192: 192 = 2⁶ × 3

What are Factors of 192?

Factors of a number are the exact divisors of the number, leaving the remainder as 0. Factors of 192 are the numbers that exactly divide 192. Let's divide 192 by 16.

• 192 ÷ 16 = 12

So, the number 16 exactly divides 192. This means 16 and 12 are the factors of 192. In fact, all such numbers are the factors of 192.

How to Calculate Factors of 192?

Now, you already know the division method to find the factors of 192. But we have another way to find the factors of 192.
In other words, factors of 192 are the numbers that, when multiplied together, give the product as 192. Can you think of all such pairs of numbers?
Look below to see some factors of 192:

Not only this, you can use a factor tree to find the factors of 192:

So, the factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192. In fact, the prime factors of 192 are 2 and 3.

Q: Can you guess two factors of 192 that up to 4?

A: The factors of 192 that add up to 4 are 1 and 3.

Explore factors using illustrations and interactive examples:

• Factors of 73 - The factors of 73 are 1, 2, 37, 74.
• Factors of 76 - The factors of 76 are 1, 2, 4, 19, 38, 76.
• Factors of 87 - The factors of 87 are 1, 3, 29, 87.
• Factors of 92 - The factors of 92 are 1, 2, 4, 23, 46, 92.
• Factors of 100 - The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50,100.

Prime factorization is a way of expressing a number as a product of its prime factors.

Examples: Follow the steps given below to find the factors of 192 using prime factorization:

• Step 1: Find the smallest prime that exactly divides 192.
• Step 2: Write the resultant after dividing 192 by the smallest prime in one column.
• Step 3: Again find the smallest prime that exactly divides the resultant obtained in step 2 and write the resultant.
• Repeat step 3 until you reach number 1.

From this figure, you can observe that the prime factors of 192 are 2 and 3. So, the prime factorization of 192 is 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3.
We can also see that 192, 96, 48, 24, 12 are the composite factors of 192.

• Q: Can you see how 32 = 2⁵, 16= 2⁴ are also factors of 192?
• Q: Can you find the other composite factors of 192?

Recollect that by Fundamental Theorem of Arithmetic, there is only one unique way to represent a number by the product of its primes.

All the factor pairs of 192 are:

• 1 × 192 = 192
• 2 × 96 = 192
• 3 × 64 = 192
• 4 × 48 = 192
• 6 × 32 = 192
• 8 × 24 = 192
• 12 × 16 = 192

Finding the product of each pair will always result in 192. So, factor pairs of 192 are (1, 192), (2, 96), (3, 64), (4, 48), (6, 32), (8, 24), and (12, 16).
The product of two negative numbers is positive. The negative factor pairs of 192 are (-1, -192), (-2, -96), (-3, -64), (-4, -48), (-6, -32), (-8, -24) and (-12, -16).

• The numbers which we multiply to get 192 are the factors of 192.
• Factors of 192 are the numbers that exactly divides 192.
• The prime factorization 192 is 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3
• The number 192 has 7 positive factor pairs.

Think Tank:

1. Miley has this jar of colorful beads. It has 192 blue beads and 108 red beads. If she wants to place the beads in identical groups without any bead left over, in how many ways can she do it?

FAQs on Factors of 192

What are Factors of 192?

The factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, and 192.

What are the Positive Pair Factors of 192?

The positive factor pairs of 192 are: (1, 192), (2, 96), (3, 64), (4, 48), (6, 32), (8, 24), and (12, 16).

What are the Negative Pair Factors of 192?

The product of two negative numbers is positive. The negative factor pairs of 192 are (-1, -192), (-2, -96), (-3, -64), (-4, -48), (-6, -32), (-8, -24), and (-12, -16).

How many Factors of 192 are there?

The number 192 has 14 factors.

What are the Factors of 192 by Prime Factorization?

The prime factorization of 192 is 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3