Question

factors and multiples sheet 4:1

1. circle the numbers below which are multiples of 4:

22 34 32 28 14 41 44

1. circle the numbers below which are factors of 20:

1 2 5 10 12 20 40

1. fill in the table below

number | multiple of 3 | factor of 36
15 | yes | no
13 | |
6 | |
10 | |
4 | |
21 | |
12 | |

1. which of the numbers below are prime numbers?

16 11 15 27 23 2

1. can you find all 6 factors of 32?

__ __

1. i am a multiple of 13. i am also an even number less than 50.

who am i? ____
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Explanation:

Question 1

Step1: Recall multiple of 4 rule

A number is a multiple of 4 if dividing it by 4 gives an integer.

Step2: Check each number

• \(22\div4 = 5.5\) (not integer)
• \(34\div4 = 8.5\) (not integer)
• \(32\div4 = 8\) (integer)
• \(28\div4 = 7\) (integer)
• \(14\div4 = 3.5\) (not integer)
• \(41\div4 = 10.25\) (not integer)
• \(44\div4 = 11\) (integer)

Step1: Recall factor definition

A factor of 20 divides 20 without remainder.

Step2: Check each number

• \(20\div1 = 20\) (no remainder)
• \(20\div2 = 10\) (no remainder)
• \(20\div5 = 4\) (no remainder)
• \(20\div10 = 2\) (no remainder)
• \(20\div12 \approx 1.67\) (remainder)
• \(20\div20 = 1\) (no remainder)
• \(20\div40 = 0.5\) (remainder)

Step1: For "Multiple of 3"

A number is a multiple of 3 if sum of digits is multiple of 3. For "Factor of 36", check if 36 is divisible by the number.

Step2: Analyze each number

• 13: \(1 + 3 = 4\) (not multiple of 3) → Multiple of 3: NO; \(36\div13 \approx 2.77\) → Factor of 36: NO
• 6: \(6\div3 = 2\) (multiple of 3) → YES; \(36\div6 = 6\) → YES
• 10: \(1 + 0 = 1\) (not multiple of 3) → NO; \(36\div10 = 3.6\) → NO
• 4: \(4\div3 \approx 1.33\) → NO; \(36\div4 = 9\) → NO (Wait, \(36\div4 = 9\)? Wait, 4×9=36? No, 4×9=36? Wait 4×9=36? Yes! Wait, 4×9=36, so 4 is a factor? Wait no, 4×9=36? Wait 4×9=36? Yes, 4×9=36. Wait, but 10: 36÷10=3.6, not integer. 4: 36÷4=9, integer. So correction:
• 4: \(4\div3 \approx 1.33\) → Multiple of 3: NO; \(36\div4 = 9\) → Factor of 36: YES? Wait no, 4×9=36? Yes, 4×9=36. So 4 is a factor of 36? Wait, 36's factors: 1,2,3,4,6,9,12,18,36. Yes, 4 is a factor. So:
• 4: Multiple of 3: NO; Factor of 36: YES
• 21: \(2 + 1 = 3\) (multiple of 3) → YES; \(36\div21 \approx 1.71\) → NO
• 12: \(1 + 2 = 3\) (multiple of 3) → YES; \(36\div12 = 3\) → YES

So the table:

NUMBER	MULTIPLE OF 3	FACTOR OF 36
13	NO	NO
6	YES	YES
10	NO	NO
4	NO	YES
21	YES	NO
12	YES	YES

Answer:

Circle 32, 28, 44

Question 2