Divisibility rule for 3
The divisibility rule for 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3. For example, 123 has digits 1 + 2 + 3 = 6, and since 6 is divisible by 3, so is 123. Covered in Saxon Math Intermediate 4, this shortcut allows students to quickly determine factors without long division, a skill that accelerates fraction simplification, prime factorization, and number theory work in Grades 5 and 6.
Key Concepts
Property A number is divisible by 3 if the sum of its digits is a multiple of 3. For example, for the number 87, we add the digits: $8 + 7 = 15$. Since 15 is a multiple of 3, the number 87 is divisible by 3.
Can 75 be divided by 3? Check: $7 + 5 = 12$. Since 12 is a multiple of 3, the answer is yes. $75 \div 3 = 25$. Can 92 be divided by 3? Check: $9 + 2 = 11$. Since 11 is not a multiple of 3, the answer is no. Can 45 be divided by 3? Check: $4 + 5 = 9$. Since 9 is a multiple of 3, the answer is yes. $45 \div 3 = 15$.
Want to know if a number can be friends with 3, meaning it divides by 3 with no leftovers? Don't guess! Just add up its digits. If that sum is in the 3 times table, like 3, 6, 9, or 12, then the original number is too! It's a super secret handshake that only multiples of 3 know.
Common Questions
What is the divisibility rule for 3?
A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 372: 3 + 7 + 2 = 12, and 12 / 3 = 4, so 372 is divisible by 3.
How do you check if a large number is divisible by 3?
Add all the digits together. If the sum is 3, 6, 9, 12, 15, or any multiple of 3, the original number is divisible by 3. Keep adding digits if the sum is still large.
Is every multiple of 9 also divisible by 3?
Yes. Every multiple of 9 is also a multiple of 3, because 9 = 3 x 3. However, not every multiple of 3 is a multiple of 9. For example, 12 is divisible by 3 but not 9.
When do students learn the divisibility rule for 3?
Students learn divisibility rules including the rule for 3 in Grade 4. Saxon Math Intermediate 4 introduces this rule to build mental math speed and prepare students for fraction simplification.
Why are divisibility rules important in math?
Divisibility rules allow students to quickly determine factors without performing long division. This speeds up simplifying fractions, finding common denominators, and identifying prime and composite numbers.
How does the divisibility rule for 3 connect to simplifying fractions?
When simplifying fractions, students need to find common factors. If both numerator and denominator pass the divisibility-by-3 test, they can both be divided by 3, simplifying the fraction.
What are other useful divisibility rules?
Divisibility by 2: even numbers (last digit 0, 2, 4, 6, or 8). Divisibility by 5: last digit is 0 or 5. Divisibility by 9: digit sum is divisible by 9. Divisibility by 10: last digit is 0.