Investigate patterns in consecutive numbers, factors, multiples, and remainders, and learn quick divisibility rules for 3, 9, and 11.
A number is divisible by 3 or 9 if the sum of its digits is divisible by 3 or 9 respectively. A number is divisible by 11 if the difference between the sum of digits in odd and even positions is 0 or a multiple of 11.
Is 4,536 divisible by 9?
4+5+3+6 = 18, which is divisible by 9, so yes
Is 2,915 divisible by 11?
Odd positions (from right): 5+1=6, Even positions: 1+9=... let's recompute: digits 2,9,1,5 → odd-position sum (1st,3rd from right)=5+1=6, even-position sum (2nd,4th)=1+9=10; difference=|6−10|=4, not a multiple of 11, so no
The digital root of a number is found by repeatedly summing its digits until a single digit remains. This is useful for quick divisibility checks and number puzzles.
Find the digital root of 7,891.
7+8+9+1=25, 2+5=7; digital root is 7
If a number's digital root is 9, what does that tell you about divisibility by 9?
The number is divisible by 9
1. Is 6,342 divisible by 3?
2. Is 837 divisible by 9?
3. Find the digital root of 48,573.
4. Is 1,331 divisible by 11?
5. What is the sum of any three consecutive numbers always divisible by?