GCF and LCM

Question 1

Decompose

Answer 1

to decompose in math is to break down numbers into parts

Question 2

Factor

Answer 2

a number that divides another number or expression evenly (into a whole number) i.e., with no remainder.

For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly

Question 3

Product

Answer 3

two or more numbers when multiplied together

the product of 3 and 6 is 18

Question 4

Prime

Answer 4

A whole number above 1 that can not be made by multiplying other whole numbers

Examples are 1, 2, 3, and 5. You can only get the product is you multiply by 1 and itself

Question 5

Composite

Answer 5

composite numbers can be defined as the whole numbers that have more than two factors

12 is a composite number because it has 1, 2, 3, 4, 6, and 12 as factors

Question 6

Proper Factor

Answer 6

A proper factor of a number is any factor of the number except the number itself.

So, if our factors of 10 were 1, 2, 5, and 10, the proper factors of the number 10 are 1, 2, and 5! Remember that 10 is not a proper factor of itself.

Question 7

Abundant Number

Answer 7

a number for which the sum of its proper divisors is greater than itself.

For example, 12 is abundant because the sum of its proper divisors is 1 + 2 + 3 + 4 + 6 = 16 > 12.

Question 8

Perfect Number

Answer 8

a positive whole number that is equal to the sum of its proper divisors.

The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128

Question 9

Deficient Number

Answer 9

the sum of the proper divisors (factors) a number that is less than itself

Examples of deficient numbers include 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, and 23.

Question 10

Square Number

Answer 10

to multiple a number by itself

9 is a square number because it is 3 x 3

Question 11

Great Common Factor

Question 12

Lowest Common Multiple

Question 13

Relatively Prime

Answer 13

when the GCF is 1 (or the only factor two numbers have in common is 1)

12 and 25 are relatively prime- their GCF is 1

Question 14

Prime Factorization

Answer 14

“Prime Factorization” is finding which prime numbers multiply together to make the original number (you need to make a factor tree to do this)

Question 15

Factor Strings

Answer 15

a number written as a product of two or more factors.

In a factor string, 1 may not be used as a factor. For example, a factor string for 24 is 2 X 3 X 4, or 2 3 4