Write all the factors of the following number:
We have hundreds of course questions with personalized recommendations + Account 100% premium
Write all the factors of the following number:
To find all the factors of the number , we'll follow these steps:
Let's proceed with the solution:
Step 1: Check divisibility by small primes.
Firstly, check for divisibility by . Since is odd, it's not divisible by .
Step 2: Check divisibility by . Add the digits of (i.e., ), which is divisible by . Thus, .
Step 3: Check for divisibility by . Because ends in , it is divisible by . So, .
Step 4: Check . This is a prime number.
Thus, the prime factorization of is .
Step 5: Now, list all the prime factors of , which are , , and .
Therefore, the factors of include exactly these prime divisors.
Hence, the solution to the problem is:
.
Write all the factors of the following number: \( 6 \)
Prime factors are the basic building blocks (like 3, 5, 41 for 615). All factors include every number that divides evenly: 1, 3, 5, 15, 41, 123, 205, and 615!
Use the prime factors to build combinations! For , multiply different combinations: 3×5=15, 3×41=123, 5×41=205, plus 1 and 615 itself.
It's a special rule! If the sum of digits is divisible by 3, the whole number is too. For 615: 6+1+5=12, and since 12÷3=4, we know 615 is divisible by 3.
Keep dividing until you reach a prime number that can't be divided further. Like 41 - test if smaller primes divide it. Since none do, 41 is prime and you're done!
Test divisibility by primes up to the square root! For 41, test primes up to √41 ≈ 6.4, so check 2, 3, 5. Since none divide evenly, 41 is prime.
Get unlimited access to all 18 Division - Advanced questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime