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The paired factors of 330 are :-

1 x 330

2 x 165

3 x 110

5 x 66

6 x 55

10 x 33

11 x 30

15 x 22

The two factors that sum to 37 are 15 & 22. The larger number is thus 22.

Alternatively, let the two numbers be a and b. Then a + b = 37, therefore a = (37 - b). Substituting for a in ab = 330 generates the quadratic equation b2 - 37b + 330 = 0.

Solving this gives b = (37 ± 7)/2 = 22 and 15. The larger number is 22.

NOTE : The equation can also be factored giving these same answers

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