Solution - Long multiplication

Start by multiplying the ones digit (7) of the multiplier 257 by each digit of the multiplicand 8,664, from right to left.

Multiply the ones digit (7) of the multiplicator by the number in the ones place value:
7×4=28

Write 8 in the ones place.

Because the result is greater than 9, carry the 2 to the tens place.

Multiply the ones digit (7) of the multiplicator by the number in the tens place value and add the carried number (2):
7×6+2=44

Write 4 in the tens place.

Because the result is greater than 9, carry the 4 to the hundreds place.

Multiply the ones digit (7) of the multiplicator by the number in the hundreds place value and add the carried number (4):
7×6+4=46

Write 6 in the hundreds place.

Because the result is greater than 9, carry the 4 to the thousands place.

Multiply the ones digit (7) of the multiplicator by the number in the thousands place value and add the carried number (4):
7×8+4=60

Write 0 in the thousands place.

Because the result is greater than 9, carry the 6 to the ten thousands place.

60,648 is the first partial product.

Proceed by multiplying the tens digit (5) of the multiplier (257) by each digit of the multiplicand (8,664), from right to left.

Because digit (5) is in tens place, we shift partial result by 1 place(s) by placing 1 zero(s).

Multiply the tens digit (5) of the multiplicator by the number in the ones place value:
5×4=20

Write 0 in the tens place.

Because the result is greater than 9, carry the 2 to the hundreds place.

Multiply the tens digit (5) of the multiplicator by the number in the tens place value and add the carried number (2):
5×6+2=32

Write 2 in the hundreds place.

Because the result is greater than 9, carry the 3 to the thousands place.

Multiply the tens digit (5) of the multiplicator by the number in the hundreds place value and add the carried number (3):
5×6+3=33

Write 3 in the thousands place.

Because the result is greater than 9, carry the 3 to the ten thousands place.

Multiply the tens digit (5) of the multiplicator by the number in the thousands place value and add the carried number (3):
5×8+3=43

Write 3 in the ten thousands place.

Because the result is greater than 9, carry the 4 to the hundred thousands place.

433,200 is the second partial product.

Proceed by multiplying the hundreds digit (2) of the multiplier (257) by each digit of the multiplicand (8,664), from right to left.

Because digit (2) is in hundreds place, we shift partial result by 2 place(s) by placing 2 zero(s).

Multiply the hundreds digit (2) of the multiplicator by the number in the ones place value:
2×4=8

Write 8 in the hundreds place.

Multiply the hundreds digit (2) of the multiplicator by the number in the tens place value:
2×6=12

Write 2 in the thousands place.

Because the result is greater than 9, carry the 1 to the ten thousands place.

Multiply the hundreds digit (2) of the multiplicator by the number in the hundreds place value and add the carried number (1):
2×6+1=13

Write 3 in the ten thousands place.

Because the result is greater than 9, carry the 1 to the hundred thousands place.

Multiply the hundreds digit (2) of the multiplicator by the number in the thousands place value and add the carried number (1):
2×8+1=17

Write 7 in the hundred thousands place.

Because the result is greater than 9, carry the 1 to the millions place.

1,732,800 is the third partial product.

60648+433200+1732800=2226648 long addition steps can be seen here

The solution is: 2,226,648