Factors of 144
Factors of 144 are the list of integers that we can split evenly into 144. There are overall 15 factors of 144, of which 2 and 3 are its prime factors. The Prime Factorization of 144 is 24 × 32.
- Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144
- Negative Factors of 144: -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72 and -144
- Prime Factors of 144: 2, 3
- Prime Factorization of 144: 2 × 2 × 2 × 2 × 3 × 3 = 24 × 32
- Sum of Factors of 144: 403
| 1. | What Are the Factors of 144? |
| 2. | How to Calculate the Factors of 144? |
| 3. | Factors of 144 in Pairs |
| 4. | Important Notes |
| 5. | FAQs on Factors of 144 |
What Are the Factors of 144?
Factors of a number are the numbers that divide the given number exactly with no remainder. Factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. So,144 is a composite number as it has factors other than 1 and itself.
How to Calculate the Factors of 144?
We can use different methods like divisibility test, prime factorization, and the upside-down division method to calculate the factors of 144. In prime factorization, we express 144 as a product of its prime factors and in the division method we divide the number by whole numbers or integers. Let us see what all numbers divide 144 exactly without a remainder.
Prime Factorization by Division Method
The upside-down division got its name so because the division symbol is flipped upside down.
- STEP 1: Using divisibility rules, we find out the smallest exact prime divisor (factor) of the given number. Here, 144 is an even number. So it is divisible by 2. In other words, 2 divides 144 with no remainder. Therefore, 2 is the smallest prime factor of 144.
- STEP 2: We divide the given number by its smallest factor other than 1 (prime factor). 144 ÷ 2= 72
- STEP 3: We then find the prime factors of the obtained quotient. Repeat Step 1 and Step 2 till we get the prime number as a quotient. In the last step, 9 is the quotient (9 ÷ 3= 3) 3 is the quotient, so we stop the process here.
Therefore, prime factorization of 144 = 2 × 2 × 2 × 2 × 3 × 3.
2 and 3 are prime factors of 14.
Explore factors using illustrations and interactive examples.
- Factors of 196 - The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, and 196.
- Factors of 110 - The factors of 110 are 1, 2, 5, 10, 11, 22, 55, and 110.
- Factors of 225 - The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.
- Factors of 35 - The factors of 35 are 1, 5, 7, and 35.
- Factors of 162 - The factors of 162 are 1,2, 3, 6, 9, 18, 27, 54, 81, and 162.
Factors of 144 in Pairs
Factor pairs of 144 are the two numbers which, when multiplied, give the number 144.
| Factors of 144 in Pairs | Notation |
|---|---|
| 1 × 144 | (1,144) |
| 2 × 72 | (2,72) |
| 3 × 48 | (3,48) |
| 4 × 36 | (4,36) |
| 6 × 24 | (6,24) |
| 8 × 18 | (8,18) |
| 9 × 16 | (9,16) |
| 12 × 12 | (12,12) |
Therefore, factors of 144 in pairs are (1,144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), and (12, 12).
We can have negative factors also for a given number.
- The product of two negative numbers is positive.
- - (×) - = +
- (-1,-144) , (-2,-72) and (-3,-48), etc., are also factor pairs of 144.
With factors, we are only looking for whole numbers that are equal to or less than the original number.
Important Notes:
- The factors of composite number 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
- 144 is a square number.
- The prime factorization of 144 is 2 × 2 × 2 × 2 × 3 × 3.
Challenging Questions
- Which of the following numbers is the product of exactly 3 distinct prime numbers?
45, 60, 91, 105, 330 - Find the least number by which 14444 would need to be multiplied to give a square number.
Factors of 144 Solved Examples
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Example 1: The area of the dining room at Thomas Jefferson’s home in Monticello is about 144 square feet. What are the possible dimensions of the room?
Solution:
The area of a rectangle is length × breadth.
Given area = 144 square feet
So, the possible length and breadth are the factor pairs of 144 (as the product of these pairs is 144).Length of Room (Feet) Breadth of Room (Feet) 1 144 2 72 3 48 4 36 6 24 8 18 9 16 12 12 (1,144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), and (12, 12).
Here, the layout of the rectangular room can be changed by swapping length by breadth. So, there are 16 possible options.
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Example 2: Help Ria find the prime factors of 144.
Solution:
The factors of composite number 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.
The prime factorization of 144 is 1 × 2 × 2 × 2 × 2 × 3 × 3.
The prime factors of 144 are 1, 2, and 3. -
Example 3: How many factors are there for 144?
Solution:
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144. Therefore, 144 has 15 factors.
FAQs on Factors of 144
What are the Factors of 144?
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 and its negative factors are -1, -2, -3, -4, -6, -8, -9, -12, -16, -18, -24, -36, -48, -72, -144.
What is the Greatest Common Factor of 144 and 92?
The factors of 144 and 92 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 and 1, 2, 4, 23, 46, 92 respectively.
Common factors of 144 and 92 are [1, 2, 4].
Hence, the GCF of 144 and 92 is 4.
What are the Common Factors of 144 and 101?
Since, the factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 and factors of 101 are 1, 101. Hence, 144 and 101 have only one common factor which is 1. Therefore, 144 and 101 are co-prime.
What is the Sum of all the Factors of 144?
Sum of all factors of 144 = (24 + 1 - 1)/(2 - 1) × (32 + 1 - 1)/(3 - 1) = 403
What numbers are the Pair Factors of 144?
The pair factors of 144 are (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), (12, 12).
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