I am a two digit number my ones digit is the double of my tens digit two of my divisor are 8and 12
To find the two-digit number that satisfies the given conditions, we can use a systematic approach.
Let's start by identifying the possible tens digits using the information given. Since the ones digit is double the tens digit, we can have the following options for the tens digit: 1, 2, 3, 4, or 5.
Now, let's check each option to see if it satisfies the condition of being divisible by 8 and 12.
For the tens digit 1:
If the tens digit is 1, then the ones digit must be 2.
The number formed is 12, which is not divisible by 8 (12 ÷ 8 = 1 remainder 4) and not divisible by 12 (12 ÷ 12 = 1 remainder 0).
For the tens digit 2:
If the tens digit is 2, then the ones digit must be 4.
The number formed is 24, which is divisible by 8 (24 ÷ 8 = 3 remainder 0) and not divisible by 12 (24 ÷ 12 = 2 remainder 0).
Therefore, the two-digit number that satisfies the conditions is 24.
Let's solve this step by step.
Step 1: Identify the two-digit number.
We know that the number has a ones digit that is twice as large as the tens digit. Let's represent the tens digit as "x" and the ones digit as "2x." Therefore, the number can be expressed as 10x + 2x = 12x.
Step 2: Find the divisors of the number.
The divisors of the number are 8 and 12. Divisors are the numbers that divide evenly into the given number.
To find the divisors of 12x, let's factorize it. 12x = 2 * 2 * 3 * x = 2^2 * 3 * x.
The divisors of 12x are all the combinations of the factors. So, the divisors can be 1, 2, 3, 4, 6, 12, x, 2x, 3x, 4x, 6x, and 12x.
Step 3: Solve for x.
Based on the given information, we know that two of the divisors are 8 and 12. Therefore, we can set up two equations:
Equation 1: 12x = 8
Equation 2: 12x = 12
Simplifying Equation 1, we divide both sides by 12:
x = 8/12
x = 2/3
Simplifying Equation 2, we divide both sides by 12:
x = 12/12
x = 1
So, the possible solutions for the tens digit (x) are 2/3 or 1.
Step 4: Find the number.
Using the possible values for the tens digit, we can calculate the ones digit (2x). Let's substitute the values of x into the equation:
For x = 2/3, the ones digit (2x) = 2 * (2/3) = 4/3. This is not a valid solution since we need a whole number.
For x = 1, the ones digit (2x) = 2 * 1 = 2.
Therefore, the possible two-digit numbers are 12 and 32, with 1 as the tens digit and 2 as the ones digit.
You can represent your number like:
x = 10 * a + b
where:
a = tens digit
b = ones digit
Two of my divisor are 8 and 12 mean you must find least common multiple of 8 and 12
Least Common Multiple ( 8 , 12 )= 24
This mean x = 24
b = 2 , a = 4
Proof:
x = 10 b + a = 24
x = 10 b + a =
10 * 2 + 4 =
20 + 4 = 24