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Question

The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example, the prime sum of 12 is 7 , since 12 = 2 \times 2 \times 3 and 2 + 2 + 3 = 7 . For which of the following integers is the prime sum greater than 35 ?

Answer Choices

A. $440$
B. $512$
C. $620$
D. $700$
E. $750$

Steps

Explanation	Calculations	Help
$We restate that the ("prime sum") of a number is defined as the sum of its prime factors, counting repetitions.$	$prime sum (n) = sum of prime factors of n including repetitions$
$We factor 440 into its prime factors.$	$440 = 44 \times 10 44 = 4 \times 11 4 = 2 \times 2 10 = 2 \times 5 440 = 2 \times 2 \times 2 \times 5 \times 11$	Theory & Tactics Method Card DIV4-C Click to view full details
$We compute the prime sum for 440.$	$2 + 2 + 2 + 5 + 11 = 22$
$We factor 512 into its prime factors using exponent notation.$	$512 = 2^{9}$	Theory & Tactics Method Card DIV4-C Click to view full details
$We compute the prime sum for 512.$	$9 \times 2 = 18$
$We factor 620 into its prime factors.$	$620 = 62 \times 10 62 = 2 \times 31 10 = 2 \times 5 620 = 2 \times 2 \times 5 \times 31$	Theory & Tactics Method Card DIV4-C Click to view full details
$We compute the prime sum for 620.$	$2 + 2 + 5 + 31 = 40$
$We factor 700 into its prime factors.$	$700 = 7 \times 100 100 = 10 \times 10 10 = 2 \times 5 700 = 2 \times 2 \times 5 \times 5 \times 7$	Theory & Tactics Method Card DIV4-C Click to view full details
$We compute the prime sum for 700.$	$2 + 2 + 5 + 5 + 7 = 21$
$We factor 750 into its prime factors.$	$750 = 75 \times 10 75 = 15 \times 5 15 = 3 \times 5 10 = 2 \times 5 750 = 3 \times 5 \times 5 \times 2 \times 5$	Theory & Tactics Method Card DIV4-C Click to view full details
$We compute the prime sum for 750.$	$3 + 5 + 5 + 2 + 5 = 20$
$We compare the prime sums and identify which exceeds 35.$	$440 : 22 512 : 18 620 : 40 700 : 21 750 : 20 40 > 35$

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Final Answer

620

Question

The "prime sum" of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example, the prime sum of 12 is 7 , since 12 = 2 \times 2 \times 3 and 2 + 2 + 3 = 7 . For which of the following integers is the prime sum greater than 35 ?

Answer Choices

A. $440$
B. $512$
C. $620$
D. $700$
E. $750$

Steps

Explanation	Calculations	Help
$We restate that the ("prime sum") of a number is defined as the sum of its prime factors, counting repetitions.$	$prime sum (n) = sum of prime factors of n including repetitions$
$We factor 440 into its prime factors.$	$440 = 44 \times 10 44 = 4 \times 11 4 = 2 \times 2 10 = 2 \times 5 440 = 2 \times 2 \times 2 \times 5 \times 11$	Theory & Tactics Method Card DIV4-C Click to view full details
$We compute the prime sum for 440.$	$2 + 2 + 2 + 5 + 11 = 22$
$We factor 512 into its prime factors using exponent notation.$	$512 = 2^{9}$	Theory & Tactics Method Card DIV4-C Click to view full details
$We compute the prime sum for 512.$	$9 \times 2 = 18$
$We factor 620 into its prime factors.$	$620 = 62 \times 10 62 = 2 \times 31 10 = 2 \times 5 620 = 2 \times 2 \times 5 \times 31$	Theory & Tactics Method Card DIV4-C Click to view full details
$We compute the prime sum for 620.$	$2 + 2 + 5 + 31 = 40$
$We factor 700 into its prime factors.$	$700 = 7 \times 100 100 = 10 \times 10 10 = 2 \times 5 700 = 2 \times 2 \times 5 \times 5 \times 7$	Theory & Tactics Method Card DIV4-C Click to view full details
$We compute the prime sum for 700.$	$2 + 2 + 5 + 5 + 7 = 21$
$We factor 750 into its prime factors.$	$750 = 75 \times 10 75 = 15 \times 5 15 = 3 \times 5 10 = 2 \times 5 750 = 3 \times 5 \times 5 \times 2 \times 5$	Theory & Tactics Method Card DIV4-C Click to view full details
$We compute the prime sum for 750.$	$3 + 5 + 5 + 2 + 5 = 20$
$We compare the prime sums and identify which exceeds 35.$	$440 : 22 512 : 18 620 : 40 700 : 21 750 : 20 40 > 35$

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Final Answer

620