Divisibility

Question 1

Yielding integer

Answer 1

given x, y
x/y will yield integer
if y is a factor of x
or if x is a multiple of y

Question 2

Instead of doing long division…

Answer 2

do prime factorization

Question 3

if x is divisible by y…

Answer 3

then x also divisible by all factors of y

Question 4

with exponents,

Answer 4

if you have the same base x, then x^Z / x^Y if x>y so that z-y = positive number

Question 5

is 14rst/18 an integer

Answer 5

PRIME FACTORIZE - because 14 and 18 do share a common factor (2)

Question 6

if x is divisible by z and y,

Answer 6

must be divisible by LCM z, Y

Question 7

World problems - W = original price; N = sales price; X% = discount

Answer 7

N = W * x/100
N / x/100 = W
W = 100N/x

Question 8

Divisibility rules

Answer 8

• 0 divisible by any no to yield 0
• no no. divisible by 0
• all no divisible by 1
• no divisible by 2 if units digit is 0, 2, 4, 6, 8
• no divisible by 3 if sum of all digits divisible by 3
• no divisible by 4 if last two digits divisible by 4. All multiples of 100 (got 00 at end) divisible by 4
• no divisible by 5 if units digit divisible by 0 or 5
• no divisible by 6 if divisible by 2 and by 3 (so even and digits sum together to something divisible by 3)
• no divisible by 7 - no tricks, just do it
• no divisible by 8 if even and last 3 digits divisible by 8, and all numbers with 000 divisible by 8
• no divisible by 9 if sum of all digits divisible by 9
• no divisible by 10 if unit digit is a zero
• no divisible by 11 is sum of odd numbered place digits minus sum of even numbered place digits is divisible by 11
• no divisible by 12 if divisible by 3 and 4 (so sum of digits divisible by 3 and last two digits divisible by 4 or 00)

Question 9

Division formula

Answer 9

X/Y = Q + R/Y

X= QY + R

R = X-QY

Question 10

You can convert fraction remainder into a decimal

Answer 10

BUT NOT vice-versa

And if you can reduce into smallest fraction form, you know actual remainder must be a multiple of that

Question 11

To convert decimal remainder into exact integer remainder

Answer 11

eg 9/5 = 1.8
take 0.8 * 5 = 4
4 is remainder