# 1712 Can You Make the Factors Fit?

Contents

### Today’s Puzzle:

This Factor Fits puzzle starts off fairly easy before it potentially might give you fits trying to place the rest of the factors. Are you game? ### Factors of 1712:

• 1712 is a composite number.
• Prime factorization: 1712 = 2 × 2 × 2 × 2 × 107, which can be written 1712 = 2⁴ × 107.
• 1712 has at least one exponent greater than 1 in its prime factorization so √1712 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1712 = (√16)(√107) = 4√107.
• The exponents in the prime factorization are 4 and 1. Adding one to each exponent and multiplying we get (4 + 1)(1 + 1) = 5 × 2 = 10. Therefore 1712 has exactly 10 factors.
• The factors of 1712 are outlined with their factor pair partners in the graphic below. ### More About the Number 1712:

1712 is the difference of two squares in three different ways:
429² – 427² = 1712,
216² – 212² = 1712, and
111² – 103² = 1712.

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