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1. Fill in the blanks.

(a) 5 x 6 = 30, so 5 and 6 are ______ of 30.

(b) 48 = 8 x 6, so 6 and 8 are ______ of 48.

(c) 12 = 2 x 2 x 3, so 2, 3, 4, and 6 are ______ of 12.

(d) 45 = 3 x 3 x 5, so 3, 5, 9, and 15 are ______ of 45.

(e) 16 and 9 are factors of 144. So 144 is ______ by 16 and 9.

Answer :

Let's fill in the blanks using the concept of factors and divisibility in mathematics.

  1. (a)
    [tex]5 \times 6 = 30[/tex], so 5 and 6 are factors of 30.

    • A factor is a number that divides into another number exactly without leaving a remainder. In this calculation, both 5 and 6 divide 30 evenly.

  2. (b)
    [tex]48 = 8 \times 6[/tex], so 6 and 8 are factors of 48.

    • Here, both 6 and 8 divide 48 without any remainder.

  3. (c)
    [tex]12 = 2 \times 2 \times 3[/tex], so 2, 3, 4, and 6 are factors of 12.

    • Breaking down 12 into its prime factors (2 and 3), as well as multiplying these primes to form other possible factors like 4 (which is [tex]2 \times 2[/tex]) and 6 (which is [tex]2 \times 3[/tex]), we see that they all divide 12 exactly.

  4. (d)
    [tex]45 = 3 \times 3 \times 5[/tex], so 3, 5, 9, and 15 are factors of 45.

    • Factorizing 45 gives us these numbers that can divide into 45 evenly. 9 is [tex]3 \times 3[/tex] and 15 is [tex]3 \times 5[/tex], both of which are stable factors.

  5. (e)
    16 and 9 are factors of 144. So 144 is divisible by 16 and 9.

    • A number is divisible by its factors without leaving a remainder. In this case, 144 can be evenly divided by both 16 and 9.

Understanding factors and divisibility is a key part of number theory in mathematics and helps in simplifying expressions, solving equations, and finding greatest common divisors.

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