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It could be 105, 112 or 133.

Having 7 as a factor means it is a multiple of 7.

The first 3 digit multiple of 7: 100 ÷ 7 = 14 2/7 → first 3 digit multiple of 7 is 15 × 7 = 105

Last 3 digit multiple of 7 less than 140: 140 ÷ 7 = 20 → last 3 digit multiple of 7 less than 140 is 19 × 7 = 133

→ The possible multiples of 7 to consider are [15..19] × 7 which gives 105, 112, 119, 126 and 133.

The sum of the digits of these number is:

105 → 1 + 0 + 5 = 6

112 → 1 + 1 + 2 = 4

119 → 1 + 1 + 9 = 11

126 → 1 + 2 + 6 = 9

133 → 1 + 3 + 3 = 7

Of these sums only 6, 4 and 7 are less than 9, thus the possible numbers are 105, 112 or 113.

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Q: What is the number that has three digits is less than 140 has 7 as a factor and the sum of the digits is less than 9?
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