Rectangle measures 72cm by108 how can use the common factors of 72 and 108 identify all the squares that can be used to cover the rectangle?
The different squares would have sides equal to the different common factors. Like, they could be 1 cm x 1 cm since 1 is a common factor. They could also be 2 cm x 2 cm, 3 x 3, 4 x 4, 6 x 6, etc
A rectangle measures 72cm by 108cm. a 2cm by 2cm square can be used to cover the rectangle without any spaces?
Divide the area of the rectangle by the area of the little squares: 72(108) / 2^2 = 1944 It would take 1944 two-by-two squares to cover the area.
The answers are already there but I'll try to rewrite them "for dummies".The first step consists of decomposing 100 into its prime factors. Since 100 = 10^2, and 10 = 2.5, we have 100 = 2^2 . 5^2.The slow but systematic way of obtaining this decomposition consists of dividing each successive quotient by its smallest prime divisor until we get down to 1, as follows:100 | 2 50 | 2 25 | 5 5 | 5 1 |Now that we know that 100 = 2^2 . 5^2, its divisors are all the products of the powers zero to two of 2 (the divisors of 2^2) by the powers zero to two of 5 (the divisors of 5^2), as follows (where x^0 = 1 for any nonzero x):2^0 . 5^0 = 12^1 . 5^0 = 22^2 . 5^0 = 42^0 . 5^1 = 52^1 . 5^1 = 102^2 . 5^1 = 202^0 . 5^2 = 252^1 . 5^2 = 502^2 . 5^2 = 100which can also be expressed in "shorthand" as100 = 1.100 = 2.50 = 4.25 = 5.20 = 10.10Best regards,Tony.
Math Factors?
all common factors will divide into the greatest common factor = 36 so the common factors are, 1,2,3,4,6,9 and those are the squares that will cover.