Multiplication Table Of 105
The table of 105 is the list of products you get when you multiply 105 by each whole number in turn. Because $105 = 3 \times 5 \times 7$, every product carries those three factors, and every product ends in either 5 or 0.
Table Of 105 Up To 10
Multiplication | Product |
|---|---|
$105 \times 1$ | 105 |
$105 \times 2$ | 210 |
$105 \times 3$ | 315 |
$105 \times 4$ | 420 |
$105 \times 5$ | 525 |
$105 \times 6$ | 630 |
$105 \times 7$ | 735 |
$105 \times 8$ | 840 |
$105 \times 9$ | 945 |
$105 \times 10$ | 1050 |
Table Of 105 Up To 20
Multiplication | Product |
|---|---|
$105 \times 11$ | 1155 |
$105 \times 12$ | 1260 |
$105 \times 13$ | 1365 |
$105 \times 14$ | 1470 |
$105 \times 15$ | 1575 |
$105 \times 16$ | 1680 |
$105 \times 17$ | 1785 |
$105 \times 18$ | 1890 |
$105 \times 19$ | 1995 |
$105 \times 20$ | 2100 |
What Is The Table Of 105 In Words?
Reading a large table aloud builds the rhythm before the digits stick.
One times 105 is 105
Two times 105 is 210
Three times 105 is 315
Four times 105 is 420
Five times 105 is 525
Six times 105 is 630
Seven times 105 is 735
Eight times 105 is 840
Nine times 105 is 945
Ten times 105 is 1050
What Is The 105 Times Table?
The 105 times table is repeated addition of 105. Each row adds one more group of 105, so the table answers "how much is one hundred five, added to itself, again and again?"
Built from the ground up, the ladder looks like this:
$105$
$105 + 105 = 210$
$105 + 105 + 105 = 315$
$105 + 105 + 105 + 105 = 420$
Multiplication is the shortcut for that stacking, which is why $105 \times 4$ and "four one-hundred-fives added together" both give 420.
What Are The Multiples Of 105?
The multiples of 105 are the numbers you reach by skip-counting in one-hundred-fives. The first twenty are:
105, 210, 315, 420, 525, 630, 735, 840, 945, 1050, 1155, 1260, 1365, 1470, 1575, 1680, 1785, 1890, 1995, 2100.
Every entry is a multiple of 105, and because $105 = 3 \times 5 \times 7$, each one is also a multiple of 3, of 5, and of 7 at the same time. That is why the products alternate between ending in 5 and ending in 0.
How To Learn The 105 Times Table (Patterns, Not Memorizing)
Bhanzu teaches the few patterns that generate a table rather than drilling its facts into recall. The table of 105 is built from numbers you already know, so you can rebuild any row by reasoning instead of storing it. Seeing that structure is the number sense that algebra later leans on.
Every pattern below comes from how 105 is composed: $105 = 100 + 5$ and $105 = 3 \times 5 \times 7$.
Pattern 1: Split it into 100 and 5. Read 105 as $100 + 5$, so $105 \times n = 100n + 5n$. For $105 \times 6$: $600 + 30 = 630$ - the distributive idea you meet again as $105(100 + 5)$ in algebra.
Pattern 2: The units digit alternates 5, 0. An odd multiplier gives a product ending in 5; an even multiplier gives one ending in 0. So $105 \times 7$ ends in 5 (735) and $105 \times 8$ ends in 0 (840), a quick check on any row.
Pattern 3: It inherits the factors 3, 5, and 7. Because $105 = 3 \times 5 \times 7$, every product is divisible by 3, by 5, and by 7. If you know the 5 times table, the 3 times table, and the 7 times table, you already hold the building blocks of the 105s.
Pattern 4: Build it from the 15 table, seven steps at a time. Since $105 = 15 \times 7$, one row of the 105s is seven rows of the 15 times table. For $105 \times 2$, take $15 \times 14 = 210$ - the same answer, reached from a smaller table you already know.
How Do You Read And Use The Table Of 105?
Read each row left to right: $105 \times 6 = 630$ is "one hundred five multiplied six times gives six hundred thirty." The first number is the group size, the second is the count of groups, and the product is the total.
To use it in reverse, divide. Asked "how many times should we multiply 105 to get 840?", compute $840 \div 105 = 8$, so the answer is 8. The place-value split is your safety net, so if a row slips, rebuild it from $100n + 5n$.
Where Does The Table Of 105 Appear?
One hundred five is the math of terms and triangles. A 15-week school term counted in 7-day weeks runs $15 \times 7 = 105$ days, so the table of 105 scales days across several such terms. The number is also the smallest odd number that is the product of three different primes ($3 \times 5 \times 7$), which is why it turns up so often in factor, divisibility, and lowest-common-multiple problems, and $105^\circ$ is a common obtuse angle in geometry (a right angle plus $15^\circ$).
Solved Examples Of The Table Of 105
Example 1
What is $105 \times 3$?
Split by place value: $100 \times 3 = 300$ and $5 \times 3 = 15$.
$300 + 15 = 315$
Final answer: $105 \times 3 = 315$.
Example 2 (Wrong path first)
A crate holds 105 bottles. How many bottles are in 8 crates?
Wrong attempt. The rusher reads $105 \times 8$ as just $100 \times 8$ and stops at 800.
Why it breaks. Dropping the 5 throws away a piece of every crate, so 800 is short by $5 \times 8 = 40$ bottles.
Correct. Add both parts: $800 + 40 = 840$.
$105 \times 8 = 840$
Final answer: 840 bottles.
Example 3
Find $105 \times 12$.
Split the multiplier: $105 \times 10 = 1050$ and $105 \times 2 = 210$.
$1050 + 210 = 1260$
Final answer: $105 \times 12 = 1260$.
Example 4
$105 \times {?} = 630$.
Divide to find the missing factor: $630 \div 105 = 6$.
Final answer: $105 \times 6 = 630$.
Example 5
A film reel runs 105 minutes. How long are 4 back-to-back screenings?
$105 \times 4 = (100 \times 4) + (5 \times 4) = 400 + 20 = 420$.
Final answer: 420 minutes, which is 7 hours.
What Are Common Mistakes With The Table Of 105?
Mistake 1: Dropping the 5 in the place-value split
Where it slips in: Using the $100 + 5$ method but multiplying only the hundred.
Don't do this: Writing $105 \times 6 = 600$ (the bare $100 \times 6$, no $5 \times 6$).
The correct way: Add both parts: $600 + 30 = 630$, so $105 \times 6 = 630$.
Mistake 2: Expecting the wrong last digit
Where it slips in: Guessing a product ends in 5 when the multiplier is even.
Don't do this: Writing $105 \times 8 = 845$.
The correct way: An even multiplier ends the product in 0, so $105 \times 8 = 840$. Odd gives 5, even gives 0 - a fast sanity read.
Practice Questions On The Table Of 105
$105 \times 3 = {?}$
$105 \times 9 = {?}$
Fill in the blank: $105 \times {?} = 1050$.
A shelf holds 105 books. How many on 6 shelves?
$105 \times 11 = {?}$
Which is larger, $105 \times 7$ or $105 \times 6$?
$105 \times 20 = {?}$
A term runs 105 days. How many days in 3 such terms?
Answers: 1. 315 2. 945 3. 10 4. 630 5. 1155 6. $105 \times 7 = 735$ is larger 7. 2100 8. 315 days.
Conclusion
The table of 105 is not a wall of facts to store but a small set of moves: split 105 into $100 + 5$, read the alternating 5-and-0 ending, and lean on the 3, 5, and 7 it is made of. Learn those, and any row from $105 \times 1 = 105$ to $105 \times 20 = 2100$ is something you can rebuild rather than recall. To take this further with a teacher, explore mental maths for kids or an elementary math tutor, and for pattern-based speed work try math programs for kids. Ready to see it taught live? Book a free demo class.
Read More
Multiplication Tables - the master hub with every times table in one place.
Tables from 1 to 20 - every chart from 2 to 20 in one grid.
Table of 21 - a factor route to 105, since $21 \times 5 = 105$.
Table of 35 - another factor route, since $35 \times 3 = 105$.
How to teach multiplication - classroom-tested ways to build table fluency.
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