Use a factor tree to write 1575 as a product of prime factors. You
should display your factor tree in your answer.
I would start with the prime 5
5*315
5*5*63
5*5*3*21
5*5*3*3*7
check that.
I don't know what a factor tree is, but I'd start by dividing by 25, which is 5x5. Any number ending in 25 or 75 is divisible by that.
1575/(5x5) = 63 = 9x7 = 3x3x7
That leads to 3x3x5x5x7 = 1575
To write 1575 as a product of prime factors using a factor tree, we need to break it down into its prime factors step by step.
Step 1:
Start with the number 1575 and find two factors that multiply to give 1575. One factor could be 3, as 3 × 525 equals 1575.
1575
/ \
3 525
Step 2:
Next, break down 525 into two factors. One factor could be 3, as 3 × 175 equals 525.
1575
/ \
3 525
/ \
3 175
Step 3:
Continue breaking down the remaining factors in the same way until all the branches end in prime numbers.
1575
/ \
3 525
/ \
3 175
/ \
5 35
Step 4:
Now, continue breaking down the remaining factors until we reach prime numbers.
1575
/ \
3 525
/ \
3 175
/ \
5 35
/ \
5 7
Step 5:
Finally, all the branches end in prime numbers. So, we can write 1575 as a product of prime factors:
1575 = 3 × 3 × 5 × 5 × 7
Hence, the prime factorization of 1575 is 3 × 3 × 5 × 5 × 7.