245×23 Base 6
To calculate 245×23 in base 6, you need to convert both numbers to base 10, calculate the multiplication, and then convert the result back to base 6.
Converting 245 to base 10:
2×6^2 + 4×6^1 + 5×6^0 = 2×36 + 4×6 + 5×1 = 72 + 24 + 5 = 101
Converting 23 to base 10:
2×6^1 + 3×6^0 = 2×6 + 3×1 = 12 + 3 = 15
Multiplying 101 × 15 = 1515 in base 10.
Converting 1515 to base 6:
1515 ÷ 6 = 252 remainder 3
252 ÷ 6 = 42 remainder 0
42 ÷ 6 = 7 remainder 0
7 ÷ 6 = 1 remainder 1
1 ÷ 6 = 0 remainder 1
The result is 110301 in base 6.
To multiply 245 by 23 in base 6, follow the steps:
Step 1: Convert both numbers to base 10.
To convert 245 from base 6 to base 10, we can use the following calculation:
2*6^2 + 4*6^1 + 5*6^0 = 72 + 24 + 5 = 101
To convert 23 from base 6 to base 10, we use the calculation:
2*6^1 + 3*6^0 = 12 + 3 = 15
So, in base 10, the problem becomes 101 * 15.
Step 2: Multiply the converted numbers in base 10.
101 * 15 = 1515
Step 3: Convert the result back to base 6.
To convert 1515 from base 10 to base 6, we can use a process of division.
Dividing 1515 by 6, we get:
1515 ÷ 6 = 252 remainder 3
Dividing 252 by 6, we get:
252 ÷ 6 = 42 remainder 0
Dividing 42 by 6, we get:
42 ÷ 6 = 7 remainder 0
Dividing 7 by 6, we get:
7 ÷ 6 = 1 remainder 1
Finally, dividing 1 by 6, we get:
1 ÷ 6 = 0 remainder 1
The remainders in reverse order are 10 (represented as 'A'), 0, 0, 1, and 1. So, the result of 245 × 23 in base 6 is A0011.
To calculate 245 multiplied by 23 in base 6, follow these steps:
Step 1: Convert the numbers from base 6 to base 10.
- Convert 245 to base 10: (2 × 6²) + (4 × 6¹) + (5 × 6⁰) = 72 + 24 + 5 = 101
- Convert 23 to base 10: (2 × 6¹) + (3 × 6⁰) = 12 + 3 = 15
Step 2: Multiply the converted numbers in base 10.
101 × 15 = 1515
Step 3: Convert the result back to base 6.
To convert 1515 to base 6, we divide it by 6 repeatedly until the quotient becomes zero. The remainders obtained, when read from bottom to top, will be the base 6 representation of the result.
1515 divided by 6 is 252 with a remainder of 3.
252 divided by 6 is 42 with a remainder of 0.
42 divided by 6 is 7 with a remainder of 0.
7 divided by 6 is 1 with a remainder of 1.
1 divided by 6 is 0 with a remainder of 1.
Reading the remainders from bottom to top, the base 6 representation of 1515 is 11030.
Therefore, 245 × 23 in base 6 is equal to 11030.