504

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Number

$504$ (five hundred and four) is:

$2^3 \times 3^2 \times 7$

The $1$st positive integer which can be expressed as the product of $2$ two-digit numbers in $2$ ways such that the factors in one of those pairs is the reversal of each of the factors in the other:

$504 = 12 \times 42 = 21 \times 24$

The $24$th positive integer after $64$, $96$, $128$, $144$, $\ldots$, $384$, $400$, $416$, $432$, $448$, $480$, $504$ with $6$ or more prime factors:

$504 = 2 \times 2 \times 2 \times 3 \times 3 \times 7$

The $37$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $\ldots$, $120$, $144$, $168$, $180$, $210$, $216$, $240$, $288$, $300$, $336$, $360$, $420$, $480$:

$\map {\sigma_1} {504} = 1560$

Also see

• Previous  ... Next: Highly Abundant Number
• Previous  ... Next: Numbers with 6 or more Prime Factors

• Next: Products of 2-Digit Pairs which Reversed reveal Same Product

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 13$: The fundamental theorem of arithmetic
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $504$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $504$