Number Sense Section 3 Formulas/Tricks

Most formulas/tricks needed from Section 3 of Bryant Heath's Number Sense guide: https://bryantheath.com/files/2018/04/Heath_NSTricks_revA.pdf

How to find the GCD of two numbers?

Find the remainder of dividing the larger number by the smaller, then find the remainder of dividing the smaller number by the previous remainder, etc.

How to find the LCM of two numbers?

Divide the numbers multiplied together by the GCD

How to find the GCD of three numbers?

Calculate the GCD of the LCM of two numbers and the third number

Sum of Coefficients of (ax+by)^n

(a+b)^n

Zeroth row of Pascal’s triangle

1

First row of Pascal’s triangle

1 1

Second row of Pascal’s triangle

1 2 1

Third row of Pascal’s triangle

1 3 3 1

Fourth row of Pascal’s triangle

1 4 6 4 1

Fifth row of Pascal’s triangle

1 5 10 10 5 1

Sixth row of Pascal’s triangle

1 6 15 20 15 6 1

Units digit rotation for powers of 2

2 4 8 6

Units digit rotation for powers of 3

3 9 7 1

Units digit rotation for powers of 4

4 6

Units digit rotation for powers of 5

5

Units digit rotation for powers of 6

6

Units digit rotation for powers of 7

7 9 3 1

Units digit rotation for powers of 8

8 4 2 6

Units digit rotation for powers of 9

9 1

log(2)

.3

log(5)

.7

ln(2)

.7

ln(10)

2.3