Question
- a) What are the prime factors of 56 ?
b) What are the composite factors of 56 ?
c) What are the square number factors of 56 ?
b) What are the composite factors of 56 ?
c) What are the square number factors of 56 ?
Ask by Blake Ross. in South Africa
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Prime Factors of 56: 2 and 7
Composite Factors of 56: 4, 8, 14, 28, 56
Square Number Factors of 56: 1 and 4
Composite Factors of 56: 4, 8, 14, 28, 56
Square Number Factors of 56: 1 and 4
Solution
Sure, let’s break down each part of your question regarding the number 56.
1. a) Prime Factors of 56
Prime factors are the prime numbers that multiply together to give the original number. To find the prime factors of 56:
- Start with the smallest prime number, 2:
- 56 ÷ 2 = 28
- Continue dividing by 2:
- 28 ÷ 2 = 14
- 14 ÷ 2 = 7
- Now, 7 is a prime number and cannot be divided further.
So, the prime factorization of 56 is:
Prime Factors of 56:
2 and 7
2 and 7
1. b) Composite Factors of 56
Composite factors are factors of a number that are composite numbers (i.e., they have more than two positive divisors). First, let’s list all the positive factors of 56:
From these, we exclude:
- 1, because it’s neither prime nor composite.
- Prime numbers, which are 2 and 7.
Composite Factors of 56:
4, 8, 14, 28, and 56
4, 8, 14, 28, and 56
1. c) Square Number Factors of 56
Square number factors are factors of 56 that are perfect squares (i.e., numbers like
Let’s identify which of these are perfect squares:
- 1 is
- 4 is
Square Number Factors of 56:
1 and 4
1 and 4
Summary:
- a) Prime Factors: 2 and 7
- b) Composite Factors: 4, 8, 14, 28, and 56
- c) Square Number Factors: 1 and 4
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To find the prime factors of 56, we break it down: 56 = 2 × 2 × 2 × 7, so the prime factors are 2 and 7.
For composite factors, they include any numbers made by multiplying the prime factors: 4 (2 × 2), 8 (2 × 2 × 2), 14 (2 × 7), and 28 (4 × 7).
The square number factors of 56 are those numbers that can be squared: the only square factors here are 1 (1²) and 4 (2²).
Now, did you know that the number 56 has been around for centuries? It’s fun to discover that it was once associated with everything from ancient measurements to shipping tons in the 18th century!
Additionally, if you’re looking to dive deeper into factors, consider trying the Sieve of Eratosthenes for finding primes. It’s a classic algorithm that can make factorization much easier and might just rekindle your love for numbers. Happy factoring!
