153

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Number

$153$ (one hundred and fifty-three) is:

$3^2 \times 17$

The sum of the first $5$ factorials:

$153 = 1! + 2! + 3! + 4! + 5!$

The $7$th Friedman number base $10$ after $25$, $121$, $125$, $126$, $127$, $128$:

$153 = 51 \times 3$

The $9$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $120$:

$153 = 1 + 5 + 9 + 13 + 17 + 21 + 25 + 29 + 33 = 9 \paren {2 \times 9 - 1}$

The $10$th pluperfect digital invariant after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, and the $1$st non-trivial one:

$1^3 + 5^3 + 3^3 = 1 + 125 + 27 = 153$

The $17$th triangular number after $1$, $3$, $6$, $10$, $15$, $21$, $28$, $36$, $45$, $55$, $66$, $78$, $91$, $105$, $120$, $136$:

$153 = \ds \sum_{k \mathop = 1}^{17} k = \dfrac {17 \times \paren {17 + 1} } 2$

The $29$th positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.

Also see

• Repeated Sum of Cubes of Digits of Multiple of 3

• Previous  ... Next: Pluperfect Digital Invariant
• Previous  ... Next: Sum of Sequence of Factorials
• Previous  ... Next: Hexagonal Number
• Previous  ... Next: Friedman Number
• Previous  ... Next: Triangular Number
• Previous  ... Next: Numbers of Zeroes that Factorial does not end with

Historical Note

$153$ was the number of fish that the disciples of Jesus hauled out of the water when Jesus suggested they put their nets over the other side of the boat.

As a result, considerable numerological interpretation has been made of this.

For example, $153$ is the $17$th triangular number.

$17$ itself is the sum of $10$, for the Ten Commandments, and $7$, the number of the Gifts of the Holy Spirit.

And so on.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $153$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $153$