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15 Jul 2026, 00:07
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(a-b)(a+b) = 3^3 * 5 *7
total factors for 945 = (3+1)(1+1)(1+1) = 16.
now since a and b can be negative as well. so total factors = 32
choice D
total factors for 945 = (3+1)(1+1)(1+1) = 16.
now since a and b can be negative as well. so total factors = 32
choice D
Bunuel
15 Jul 2026, 00:21
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So 945=a^2-b^2=(a-b)(a+b)
let x=a-b, y=a+b which makes xy=945
a=x+y/2, b=y-x/2
so a and b are integers if x and y are both odds or both even
since 945 is odd, every factor pair that * to it must both be odd making every factor pair of 945 yield integer a and b.
prime factor of 945=9*10=3^2*3*5*7=3^3*5^1*7^1
how many positive divisors (3+1)*(1+1)*(1+1)=4*2*2=16
Since x and y can both be negative, i multiply the positive factor by 2
16*2=32
ANS: D. 32
let x=a-b, y=a+b which makes xy=945
a=x+y/2, b=y-x/2
so a and b are integers if x and y are both odds or both even
since 945 is odd, every factor pair that * to it must both be odd making every factor pair of 945 yield integer a and b.
prime factor of 945=9*10=3^2*3*5*7=3^3*5^1*7^1
how many positive divisors (3+1)*(1+1)*(1+1)=4*2*2=16
Since x and y can both be negative, i multiply the positive factor by 2
16*2=32
ANS: D. 32
ajain31
Joined: 09 Nov 2024
Last visit: 06 Sep 2026
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15 Jul 2026, 00:35
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use the difference of squares
x=a-b
y = a+b
xy = 945
factorise 945 = 3^3 x 5 x 7
number of positive divisors of 945 is (3+1)(1+1)(1+1) = 16
the negative divisors of x are also 16 so total 32.
as 945 is odd both x and y are odd meaning a and b are noth integers,, thus every ordered factor pair produces one valid ordered pair. So 32.
x=a-b
y = a+b
xy = 945
factorise 945 = 3^3 x 5 x 7
number of positive divisors of 945 is (3+1)(1+1)(1+1) = 16
the negative divisors of x are also 16 so total 32.
as 945 is odd both x and y are odd meaning a and b are noth integers,, thus every ordered factor pair produces one valid ordered pair. So 32.
15 Jul 2026, 01:42
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Given: a^2 − b^2 = 945
a2 − b2 = (a − b)(a + b)
So, (a − b)(a + b) = 945
Let: x = a − b and y = a + b
Then ----> xy = 945
Also,
a = (x + y)/2
b = (y − x)/2
For a and b to be integers x and y must have the same parity. Since 945 = 3^3 × 5 × 7 is odd, all of its factor pairs are odd, so this condition is automatically satisfied.
Now counting the ordered factor pairs of 945.
Number of positive divisors of 945:
-----> (3 + 1)(1 + 1)(1 + 1)
-----> 4 × 2 × 2
-----> 16
Each positive divisor gives one positive factor pair (x, y), so there are 16 positive ordered pairs. Since both factors can also be negative, there are another 16 ordered pairs. Total ordered factor pairs = 16 + 16 = 32. Each factor pair gives exactly one ordered pair (a, b).
Answer: D.
a2 − b2 = (a − b)(a + b)
So, (a − b)(a + b) = 945
Let: x = a − b and y = a + b
Then ----> xy = 945
Also,
a = (x + y)/2
b = (y − x)/2
For a and b to be integers x and y must have the same parity. Since 945 = 3^3 × 5 × 7 is odd, all of its factor pairs are odd, so this condition is automatically satisfied.
Now counting the ordered factor pairs of 945.
Number of positive divisors of 945:
-----> (3 + 1)(1 + 1)(1 + 1)
-----> 4 × 2 × 2
-----> 16
Each positive divisor gives one positive factor pair (x, y), so there are 16 positive ordered pairs. Since both factors can also be negative, there are another 16 ordered pairs. Total ordered factor pairs = 16 + 16 = 32. Each factor pair gives exactly one ordered pair (a, b).
Answer: D.
