explain why 156 is or is not divisible by 3
To determine whether 156 is divisible by 3 or not, we need to check if the sum of its digits is divisible by 3.
The sum of the digits in 156 is:
1 + 5 + 6 = 12.
Since 12 is divisible by 3 (12 ÷ 3 = 4), we can conclude that 156 is divisible by 3.
what is the greatest common factor of 48 and 60 show your work
To find the greatest common factor (GCF) of 48 and 60, we can use the method of prime factorization.
Prime factorization of 48:
48 can be divided by 2, resulting in 24.
24 can be divided by 2, resulting in 12.
12 can be divided by 2, resulting in 6.
6 can be divided by 2, resulting in 3.
So, the prime factorization of 48 is 2^4 * 3.
Prime factorization of 60:
60 can be divided by 2, resulting in 30.
30 can be divided by 2, resulting in 15.
15 can be divided by 3, resulting in 5.
So, the prime factorization of 60 is 2^2 * 3 * 5.
Now, we can find the common factors by taking the product of the common prime factors with the lowest exponents:
Common factors: 2^2 * 3 = 12.
Therefore, the greatest common factor of 48 and 60 is 12.
Can you simplify it and make it sound like a 6th grader
Sure! To find the greatest common factor (GCF) of 48 and 60, we need to see which numbers can divide into both of them. We start by breaking down each number into its prime factors.
The prime factors of 48 are 2, 2, 2, and 2 (or 2^4), and 3.
The prime factors of 60 are 2, 2, 3, and 5.
Then, we look for the common prime factors in both numbers. In this case, the common prime factors are 2 and 3.
To find the GCF, we multiply the common prime factors together: 2 * 2 * 3 = 12.
So, the greatest common factor of 48 and 60 is 12.
To determine whether a number is divisible by 3 or not, we can use the divisibility rule for 3. According to the rule, a number is divisible by 3 if the sum of its digits is divisible by 3.
Let's apply this to the number 156:
1 + 5 + 6 = 12
The sum of the digits of 156 is 12. Now, we need to check if 12 is divisible by 3.
To do this, we can calculate the remainder when 12 is divided by 3:
12 ÷ 3 = 4 with a remainder of 0.
Since the remainder is 0, we can conclude that 156 is divisible by 3.
In summary, 156 is divisible by 3 because the sum of its digits, which is 12, is divisible by 3.