72
Dividing 72 by a growth rate gives roughly the years an investment takes to double. The exact constant is nearer 69.3; 72 is used because it divides by 2, 3, 4, 6, 8, 9 and 12. It is also the atomic number of hafnium.
- Even
- Composite
Where 72 fits
Why 72 is special
72's exceptionally high divisor count (12 divisors) is exactly what makes the Rule of 72 a practical mental-maths shortcut for compound-interest doubling times.
Same number, different meanings
How 72 is understood across different contexts — never implying one meaning because of another.
- Mathematics
72's exceptionally high divisor count (12 divisors) is exactly what makes the Rule of 72 a practical mental-maths shortcut for compound-interest doubling times.
- Everyday life
Dividing seventy-two by an annual growth rate gives an approximate doubling time, accurate enough for mental arithmetic at rates between about six and ten percent. The number is chosen for divisibility rather than precision.
- Finance & economics
The number used to estimate how long an investment takes to double is 72 (worldwide, as an approximation). Divide 72 by the annual percentage rate and the answer is roughly the doubling time in years. It works because the natural logarithm of two is about 0.693, and 72 has more small divisors than 69 does.
- Religion & belief
In Kabbalistic Judaism, a seventy-two-part name of God is derived from three verses of Exodus, each of seventy-two letters, read in alternating directions. A medieval mystical construction rather than a biblical one. The verses are scriptural; the reading that produces the name is not. This is a scholarly account rather than the tradition's own framing.
- Science
72 is the atomic number of hafnium. It absorbs neutrons well enough to serve as nuclear reactor control rods, and hafnium oxide replaced silicon dioxide as the insulating layer in modern microchips.
72 is part of
Factors & digit properties
- Divisors (12)
- 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
- Prime factorisation
- 2^3 × 3^2
- Digit sum
- 9
- Digital root
- 9
Representations
- Decimal
- 72
- Scientific notation
- 7.200 × 10^1
Roman numerals
L X X I I
Binary
1 0 0 1 0 0 0
1 × 64 + 0 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 72
Octal
1 1 0
1 × 64 + 1 × 8 + 0 × 1 = 72
Hexadecimal
4 8
4 × 16 + 8 × 1 = 72
Read as powers of two: 64 + 8 = 72.
In historical numeral systems
Egyptian
7 hobbles, 2 strokes
7 × 10 + 2 × 1 = 72. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
1 vertical wedge (sixties place), 1 corner wedge + 2 vertical wedges (units place)
1 × 60 + 12 = 72. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
omicron, then beta, marked as a numeral
omicron-beta + keraia
omicron + beta written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
ayin, then bet
ayin-bet
ayin (70) + bet (2) = 72, written in descending order.
Chinese numerals
qī shí èr
qī shí èr
七 before 十 multiplies it: 7 tens. 二 after it adds 2. The written form mirrors the arithmetic — "qī shí èr". The financial (anti-fraud) form is 柒拾貳.
Maya
3 dots (upper, twenties place) over 2 bars + 2 dots (lower, units place)
3 × 20 + 12 = 72. Places stack vertically with the smallest at the bottom, so the upper group is worth twenty times the lower.
Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.
Other mathematical patterns
- Abundant number
- Powerful number
- Harshad (Niven) number
Related numbers & connections
36 is a factor of 72 (36 × 2 = 72).
View 36 →72 appears in Numbers in culture and belief, the topic covering numbers that carry a documented cultural fact.
The rule of seventy-two estimates doubling time from a percentage, so it is read against a base of one hundred.
View 100 →Everyday life
Dividing seventy-two by an annual growth rate gives an approximate doubling time, accurate enough for mental arithmetic at rates between about six and ten percent. The number is chosen for divisibility rather than precision.
DocumentedEveryday lifeGeography: GlobalPeriod: described from 1494
Finance & economics
The number used to estimate how long an investment takes to double is 72 (worldwide, as an approximation). Divide 72 by the annual percentage rate and the answer is roughly the doubling time in years. It works because the natural logarithm of two is about 0.693, and 72 has more small divisors than 69 does.
DocumentedFinance & economicsGeography: worldwide, as an approximationThe 'Rule of 72' is a widely used finance shortcut: dividing 72 by an annual interest-rate percentage gives an approximate number of years for an investment to double through compound growth.
Widely documentedFinance & economics
Mathematics
The exact doubling-time constant for compound growth is not 72 but about 69.3, the natural logarithm of 2 times 100. 72 is used instead because it divides evenly by 2, 3, 4, 6, 8, 9 and 12 while 69 divides by almost nothing, and because the approximation is at its most accurate near 8 per cent rather than at zero. It is a case of a number being chosen for arithmetic convenience over precision.
DocumentedMathematics
Religion & belief
In Kabbalistic Judaism, a seventy-two-part name of God is derived from three verses of Exodus, each of seventy-two letters, read in alternating directions. A medieval mystical construction rather than a biblical one. The verses are scriptural; the reading that produces the name is not. This is a scholarly account rather than the tradition's own framing.
Tradition / practiceReligion & beliefCulture: Kabbalistic JudaismPresented as belief or tradition, not as an established fact.
Science
72 is the atomic number of hafnium. It absorbs neutrons well enough to serve as nuclear reactor control rods, and hafnium oxide replaced silicon dioxide as the insulating layer in modern microchips.
DocumentedScience
Common questions
What is the Rule of 72?
Divide 72 by an annual growth rate as a percentage and you get roughly the years it takes to double: 6 per cent doubles in about twelve years. The mathematically exact constant is about 69.3, not 72 — but 72 divides evenly by 2, 3, 4, 6, 8, 9 and 12 where 69 divides by almost nothing, and the approximation is most accurate around 8 per cent anyway. It is a number chosen for mental arithmetic over precision.
Is 72 a prime number?
No, 72 is not prime.
What are the factors of 72?
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
What is 72 in Roman numerals?
72 in Roman numerals is LXXII.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 6 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026