Understanding factors can be very helpful in math. Factors are numbers that divide evenly into another number. Today, let's explore the factors of 87. We'll break down what factors are, how to find them, and why prime factorization is important.
What Are Factors?
Factors are numbers that we can multiply together to get another number. For example, the factors of 6 are 1, 2, 3, and 6. This is because 1 times 6 equals 6, and 2 times 3 equals 6. Factors can be very handy in different areas of math, like solving equations and simplifying fractions.
Factors of 87
The factors of 87 are the numbers that can divide 87 without leaving a remainder. Here are the factors:
- 1
- 3
- 29
- 87
How To Calculate The Factors of 87
To calculate the factors of 87, we need to find every number that divides 87 without leaving any leftovers. This means that when we divide, the result should be a whole number. Let's go through this step by step.
The Multiplication Method
In the multiplication method, we try to find pairs of numbers that multiply to give us 87.
- Starting Small: Begin with 1, which is a factor of every number. 1 times 87 equals 87.
- Next Steps: Move on to 2. Since 87 is an odd number, it is not divisible by 2.
- Continue: Check 3. Since 87 divided by 3 equals 29, both 3 and 29 are factors.
- Further Steps: Check other numbers. None of them work until we reach 87 itself.
By checking each number up to 87, we find that only 1, 3, 29, and 87 work.
The Division Method
In the division method, we again find which numbers divide 87 without a remainder.
- Start With 1: Any number divided by 1 equals itself, so 1 and 87 are factors.
- Move To 2: Check if 87 is even. It’s not, so ignore 2.
- Check 3: Divide 87 by 3. Since 87 divided by 3 equals 29 without a remainder, both 3 and 29 are factors.
- Continue Checking: Numbers up to 87 that divide perfectly into 87 are checked next. None other than 1, 3, 29, and 87 work.
What Is Prime Factorization?
Prime factorization is the process of breaking down a number into its prime number factors. Prime numbers are numbers that can only be divided by 1 and themselves. For example, the prime factors of 20 are 2, 2, and 5 because 2 times 2 times 5 equals 20.
Prime Factors of 87
The prime factors of 87 are:
- 3
- 29
This means that 3 and 29 are prime numbers that can be multiplied together to get 87.
Conclusion
Understanding the factors of 87 is easy once you break it down step by step. By both multiplication and division methods, we found that the factors of 87 are 1, 3, 29, and 87. Using prime factorization, we also identified that 3 and 29 are the prime factors. Knowing factors can be very useful, especially in simplifying problems and working with numbers in math.
FAQs
Q1: What are factors?
A1: Factors are numbers that you can multiply together to get another number.
Q2: Why is 2 not a factor of 87?
A2: Because 87 is an odd number, it is not divisible by 2.
Q3: What is prime factorization?
A3: Prime factorization is breaking down a number into its prime number factors, which can only be divided by 1 and themselves.
Q4: Are 1 and 87 always factors?
A4: Yes, 1 and the number itself are always factors of any given number.
Q5: Can factors be negative?
A5: Yes, factors can be negative. For 87, the negative factors would be -1, -3, -29, and -87.
