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what is 58 divisible by

what is 58 divisible by

less than a minute read 05-02-2025
what is 58 divisible by

The question "What is 58 divisible by?" is essentially asking us to find the factors of 58. Factors are numbers that divide evenly into another number without leaving a remainder. Let's explore how to find these factors.

Understanding Divisibility

Before diving into the specific factors of 58, let's briefly review the concept of divisibility. A number is divisible by another number if the result of the division is a whole number (no decimals or fractions). For example, 12 is divisible by 3 because 12 ÷ 3 = 4.

Finding the Factors of 58

To find the factors of 58, we can use a few methods:

Method 1: Trial and Error

This method involves systematically testing different numbers to see if they divide evenly into 58. We start with the smallest whole number greater than 1 and work our way up.

  • 1: 58 ÷ 1 = 58 (1 is a factor of every number)
  • 2: 58 ÷ 2 = 29 (2 is a factor because 58 is an even number)
  • 29: 58 ÷ 29 = 2 (29 is a factor)
  • Numbers greater than 29: Any number greater than 29 will not divide evenly into 58.

Method 2: Prime Factorization

This method involves breaking down the number into its prime factors. Prime factors are prime numbers (numbers only divisible by 1 and themselves) that multiply together to give the original number.

  • Find the smallest prime factor: The smallest prime factor of 58 is 2.
  • Divide by the prime factor: 58 ÷ 2 = 29
  • Check if the result is prime: 29 is a prime number.

Therefore, the prime factorization of 58 is 2 x 29.

Listing the Factors

Based on the above methods, the factors of 58 are: 1, 2, 29, and 58. These are all the whole numbers that divide evenly into 58.

Conclusion: 58 is Divisible By...

To answer the initial question, 58 is divisible by 1, 2, 29, and 58. These are its only factors. Understanding factors and divisibility is fundamental in mathematics, impacting various areas like algebra, fractions, and more.

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