Divisibility/Factoring Rules Flashcards
How do you know if a number is divisible by 2?
Always an even number
Number ends in 0, 2, 4, 6, 8
How do you know if a number is divisible by 3?
Sum of the digits is a multiple of 3.
Ex: 264 = 2+6+4 = 12
12 is divisible by 3.
Ex: 9,567 = 9+5+6+7 = 27
27 is divisible by 3.
How do you know if a number is divisible by 4?
Even number with the last 2 digits divisible by 4 (or divisible by 2 twice). Also, numbers ending in “00” are divisible by 4.
Ex: 100
Ex: 7192 = 92 / 4 = 23
7192 = 92 / 2 = 46 / 2 = 23
How do you know if a number is divisible by 5?
Last digit is 0 or 5.
How do you know if a number is divisible by 6?
Number is divisible by 2 AND 3. Therefore, ends in an even number (0,2,4,6,8) AND the last two digits are a multiple of 3.
Ex: 178 = 7+8= 15 = divisible by 3
Original number is an even integer.
How do you know if a number is divisible by 7?
No trick to determine this… sorry!
How do you know if a number is divisible by 8?
Last digit is an even integer AND last 3 digits are divisible by 8 (or by 2 three times).
Ex: 67,844 = 844 = 8+4+4 = 16
Last 3 digits are divisible by 8
Original integer ends in an even number.
How do you know if a number is divisible by 9?
The sum of all the digits is a multiple of 9.
Ex: 76,248 = 7+6+2+4+8 = 27
Sum is divisible by 9.
Finding common factors:
Reduce a • b / a • c = ?
b / c
a was a common factor that could be eliminated.
Prime factorization:
Reduce 42 to is prime factors.
42 = 6 • 7
= 2 • 3 • 7
