7 (number)

← 6 7 8 →
-1 0 1 2 3 4 5 6 7 8 9 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	seven
Ordinal	7th; (seventh)
Numeral system	septenary
Factorization	prime
Prime	4th
Divisors	1, 7
Greek numeral	Ζ´
Roman numeral	VII
Roman numeral (unicode)	Ⅶ, ⅶ
Greek prefix	hepta-/hept-
Latin prefix	septua-
Binary	1112
Ternary	213
Quaternary	134
Quinary	125
Senary	116
Octal	78
Duodecimal	712
Hexadecimal	716
Vigesimal	720
Base 36	736
Greek numeral	Z, ζ
Amharic	፯
Arabic	٧,7
Germanic Variant	7
Persian	٧ - هفت
Urdu
Bengali	৭
Chinese numeral	七(qi)
Devanāgarī	७ (saat)
Telugu	౭
Tamil	௭
Hebrew	ז (Zayin)
Khmer	៧
Thai	๗

The number seven is a natural number that comes after six and before eight. In Roman numerals, it is VII.

Pronunciation of the number 7

MathematicsEdit

In mathematics, the number seven is an odd number and a prime number. It is also a Mersenne prime.

Divisibility RuleEdit

To test if an integer is divisible by 7 or not,

Take off the last digit and multiply it by 2.
Subtract that product from the root number (the integer without the last digit).^[1]
Repeat the second step again and again until it is clearly that the number is divisible by 7 or not.

Example

918785

5×2=10, 91878-10=91868
8×2=16, 9186-16=9170
0×2=0, 917-0=917
7×2=14, 91-14=77

77 is divisible by 7, so the original number 918785 is also divisible by 7.

Proof: Pretend $a$ is the root number and $b$ is the last digit. Then $10a+b$ is the whole number. If the whole number ( $10a+b$ ) is divisible by 7, $3a+b$ is also a multiple of 7. And $(3a+b)-7b=3a-6b$ is also a multiple 7. That proves $3a-6b$ is divisible by seven, since 3 and 6 are both multiples of 3. So $a-2b$ is also divisible by 7.