Factors of 34 - Definition, Examples, Quiz, FAQ, Trivia
Learn how to find factors, prime factors, and factor pairs with examples and activities
What are Factors?
Factors are numbers that you can multiply together to get another number. For example, factors of 34 are numbers that divide 34 exactly without leaving a remainder.
Think of factors like teams that can share 34 cookies equally. If you have 34 cookies, how many equal groups can you make?
The factors of 34 are 1, 2, 17, and 34. This means:
- 1 × 34 = 34
- 2 × 17 = 34
- 17 × 2 = 34
- 34 × 1 = 34
Key Concept
A factor is a whole number that divides exactly into another number without leaving a remainder.
How to Find Factors of 34
You can find the factors of 34 by dividing 34 by all whole numbers from 1 to 34 and seeing which ones divide evenly (with no remainder).
Let's try:
- 34 ÷ 1 = 34 (so 1 and 34 are factors)
- 34 ÷ 2 = 17 (so 2 and 17 are factors)
- 34 ÷ 3 = 11.333 (not a whole number, so 3 is not a factor)
- 34 ÷ 4 = 8.5 (not a whole number)
- 34 ÷ 17 = 2 (already found)
- 34 ÷ 34 = 1 (already found)
Remember
Every number has at least two factors: 1 and itself. Since 34 has more than two factors, it is called a composite number.
Prime Factorization of 34
Prime factorization means breaking down a number into its prime factors (factors that are prime numbers). Prime numbers are numbers greater than 1 that have no factors other than 1 and themselves.
Let's find the prime factors of 34:
- 34 can be divided by 2 (the smallest prime factor of 34)
- 34 ÷ 2 = 17
- 17 is a prime number (its only factors are 1 and 17)
- So the prime factors of 34 are 2 and 17
-
34
- 17
- 2
Prime Factorization
The prime factors of 34 are 2 and 17
Factor Pairs of 34
Factor pairs are two numbers that multiply together to make the original number. For 34, we have:
Positive Factor Pairs:
Remember
The factor pairs of 34 are (1, 34) and (2, 17). When we list factors, we usually list the positive factors.
Factors Practice Quiz
Test your knowledge about factors of 34 with this 5-question quiz. Choose the correct answer for each question.
Frequently Asked Questions
Here are answers to common questions about factors of 34:
Number Trivia
Discover interesting facts about the number 34 and factors:
Historical Significance
In mathematics, 34 is the ninth distinct semiprime, which means it's a product of exactly two prime numbers (2 × 17). Semiprimes have important applications in cryptography.
In Nature
34 is the atomic number of selenium, a chemical element important for human health. Selenium helps protect cells from damage and supports thyroid function.
In Sports
The number 34 has been worn by many famous athletes, including baseball Hall of Famer Nolan Ryan and hockey legend John Tonelli. It's considered a powerful number in sports.
Mathematical Properties
34 is a magic number in mathematics! It's the smallest number that can be expressed as the sum of two distinct primes in two different ways: 3+31 and 5+29 (and also 11+23 and 17+17).
