A factor of a number is an integer that divides the number exactly without leaving any remainder.
In other words:
⭐ 5 Solved Examples of Factors (With Explanation)
12 = 1 × 12
12 = 2 × 6
12 = 3 × 4
✔ Factors: 1, 2, 3, 4, 6, 12
15 = 1 × 15
15 = 3 × 5
✔ Factors: 1, 3, 5, 15
Prime factorization:
24 = 2³ × 3¹
Number of factors = (3+1)(1+1) = 8
✔ Factors: 1,2,3,4,6,8,12,24
63 ÷ 7 = 9 (no remainder)
✔ Yes, 7 is a factor of 63
154 ÷ 11 = 14 (exact)
✔ Yes, 11 divides 154 exactly and is a factor
📝Explanation:
9 × 2 = 18 → 9 divides 18 exactly.
Other numbers do not divide 18 without remainder.
📝 Description:
10 = 2 × 5 → prime factorization gives (1+1)(1+1)=4 factors → 1,2,5,10
📝 Description:
7 does not divide 36 exactly.
36 ÷ 7 = non-integer.
All other options divide 36 evenly.
📝 Description:
1 divides all integers.
0 is never a factor; the number itself is always the largest factor.
📝 Description:
4 × 5 = 20 → valid factor pair.
Other pairs do not multiply to 20.
📝 Description: 17 is a prime number → only factors are 1 and 17.
📝 Description:
45 ÷ 9 = 5 → exact division.
Others do not divide 45.
📝 Description: 32 = 4 × 8 → 8 divides 32 exactly.
📝 Description: Only perfect squares of prime numbers have exactly 3 factors.
4 = 2² → factors: 1, 2, 4
📝 Description:
50 ÷ 15 ≠ integer.
Other options divide 50 exactly.
📝 Description:
36 = 2² × 3²
Number of factors = (2+1)(2+1)=9
📝 Description:
24 ÷ 4 = 6
36 ÷ 4 = 9
4 divides both numbers; 12 does not divide 24 exactly.
📝 Description:
Every number is its own largest factor.
49 ÷ 49 = 1 (exact).
📝 Description: All even numbers are divisible by 2.
📝 Description: Every multiple of 9 is divisible by both 3 and 9.
So 3 is always a factor.
📝 Description: 100 ÷ 20 = 5 (exact), so 20 is a factor.
📝 Description: A number with exactly 2 factors (1 and itself) is prime.
📝 Description: 9 × 8 = 72 → valid factor pair.
📝 Description: 121 = 11 × 11 → 11 is a factor.
📝 Description:
Number of factors:
16 = 5 factors
18 = 6 factors
20 = 6 factors
21 = 4 factors
20 and 18 both have 6 factors, but 20’s factors are larger in value, commonly preferred answer: 20
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