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Multiply $267$ and $354$

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Greatest common factor

Full solution

Q. Multiply

267

and

354

Set up multiplication problem: Set up the multiplication problem. $\newline$ We need to multiply $267$ by $354$ .
Multiply units digit: Multiply the units digit of the second number by each digit of the first number. $\newline$ $4$ (from $354$ ) multiplied by $7$ (from $267$ ) equals $28$ , write down $8$ and carry over $2$ . $\newline$ $4$ multiplied by $6$ equals $24$ , plus the carried over $2$ equals $354$ $1$ , write down $6$ and carry over $2$ . $\newline$ $4$ multiplied by $2$ equals $8$ , plus the carried over $2$ equals $354$ $8$ , write down $354$ $8$ . $\newline$ The partial product is $7$ $0$ .
Multiply tens digit: Multiply the tens digit of the second number by each digit of the first number, remembering to add a zero before writing the new partial product (since we are now in the tens place). $\newline$ $5$ (from $354$ ) multiplied by $7$ (from $267$ ) equals $35$ , write down $5$ and carry over $3$ . $\newline$ $5$ multiplied by $6$ equals $30$ , plus the carried over $3$ equals $354$ $1$ , write down $3$ and carry over $3$ . $\newline$ $5$ multiplied by $354$ $5$ equals $354$ $6$ , plus the carried over $3$ equals $354$ $8$ , write down $354$ $8$ . $\newline$ The partial product is $7$ $0$ , but remember to add a zero before writing it down, so it becomes $7$ $1$ .
Multiply hundreds digit: Multiply the hundreds digit of the second number by each digit of the first number, remembering to add two zeros before writing the new partial product (since we are now in the hundreds place). $\newline$ $3$ (from $354$ ) multiplied by $7$ (from $267$ ) equals $21$ , write down $1$ and carry over $2$ . $\newline$ $3$ multiplied by $6$ equals $18$ , plus the carried over $2$ equals $354$ $1$ , write down $354$ $2$ and carry over $2$ . $\newline$ $3$ multiplied by $2$ equals $6$ , plus the carried over $2$ equals $354$ $8$ , write down $354$ $8$ . $\newline$ The partial product is $7$ $0$ , but remember to add two zeros before writing it down, so it becomes $7$ $1$ .
Add partial products: Add all the partial products together. $\newline$ $1068$ $\newline$ $133500$ $\newline$ $8001000$ $\newline$ --------- $\newline$ Adding these together, we get: $\newline$ $1068$ $\newline$ $133500$ $\newline$ $8001000$ $\newline$ --------- $\newline$ $94668$ (This is incorrect, let's correct it in the next step)

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