Number reference
220 explained.
220: two hundred twenty, composite; factors, prime factorization, roots, binary, hexadecimal, and digit properties.
Identity and representations
- Written form
- two hundred twenty
- Classification
- composite
- Factors
- 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, 220
- Prime factorization
- 2 × 2 × 5 × 11
- Square root
- 14.832397
- Cube root
- 6.036811
- Binary
- 11011100
- Octal
- 334
- Hexadecimal
- DC
- Roman numeral
- CCXX
- Digit sum
- 4
- Digital root
- 4
What makes 220 notable
- Factor structure. 220 breaks down into 3 distinct primes (2, 5, 11) and has 12 divisors in total, so it can be split into equal whole-number groups 10 ways beyond 1 and itself.
220 in everyday use
Two hundred twenty is half of the oldest known amicable pair. The proper divisors of 220 — 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, and 110 — add up to 284, and the proper divisors of 284 add up to 220. The Pythagoreans knew the pair, medieval Arab mathematicians found a rule for generating others, and Euler added dozens more; a schoolboy, Nicolò Paganini, found the overlooked pair 1,184 and 1,210 in 1866. In practical life 220 volts is the nominal mains voltage in much of the world.
Factored, 220 is 2² × 5 × 11. It is also the tenth tetrahedral number, so 220 spheres stack into a triangular pyramid with ten layers, and it is the sum of four consecutive primes: 47 + 53 + 59 + 61. In Genesis, Jacob's gift to Esau includes 220 goats and 220 sheep, a detail medieval commentators linked to the amicable pair. Its digit sum is 4 and it is CCXX in Roman numerals.
Nearby numbers
How to read this page
The factor list shows every way 220 splits into equal whole-number groups — 12 divisors in total. The prime factorisation is the compact form of that same information, and the base conversions restate 220 for contexts that do not use decimal.
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