Factoring and Multiples

To express 36 as a product of prime factors, we first break it down into its prime factors: 2 x 2 x 3 x 3. This simplifies to 2^2 x 3^2 in index form, where the exponents represent the number of times each prime factor is multiplied.

The factors of 60 are:

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The factors of 150 are:

1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150

The common factors are:

1, 2, 3, 5, 6, 10, 15, 30

The Greatest Common Factor:

GCF = 30

To find the common factors of 9 and 18, we first need to list the factors of each number. The factors of 9 are 1, 3, and 9, while the factors of 18 are 1, 2, 3, 6, 9, and 18. The common factors of 9 and 18 are 1, 3, and 9. Adding these common factors together gives us a sum of 13.

Ah, the least common multiple is the smallest number that all three numbers can divide into evenly. Let's see, the multiples of 5 are 5, 10, 15, 20, and so on. The multiples of 12 are 12, 24, 36, and so forth. And the multiples of 11 are 11, 22, 33, and more. So, the least common multiple of 5, 12, and 11 would be their smallest shared multiple, which is 660.

Oh, what a happy little question! To write 500 as a fraction, you can simply put it over 1 to create 500/1. This is because any whole number can be written as a fraction by putting it over 1. Just like that, you've turned 500 into a fraction, and there are so many more possibilities waiting for you on your creative math journey!

The Study Link answers for 5th grade Everyday Mathematics can typically be found in the back of the student journal or textbook. These answers are usually provided to help students check their work and understand the concepts better. Additionally, some schools or teachers may also provide access to online resources or answer keys for further assistance with the Study Link activities.

1 x 61 = 61. 61 is a prime number having no factors other than 1 and itself.

Well, isn't that a lovely little math problem we have here? Let's see, to find two numbers that multiply together to equal 1005, we can break it down into its factors. After a bit of happy math, we find that 45 times 23 equals 1005. Happy little numbers, just waiting to be discovered!

1 x 164, 2 x 82, 4 x 41.

To find the highest common factor (HCF) between 30,210 and 700, we first need to find the prime factors of each number. The prime factors of 30,210 are 2 x 3 x 5 x 7 x 11 x 17, and the prime factors of 700 are 2 x 2 x 5 x 5 x 7. To determine the HCF, we identify the common prime factors between the two numbers, which are 2, 5, and 7. Multiplying these common factors together gives us the HCF of 70.

Oh, dude, you've got a couple of options here. So, multiples of 12 are 12, 24, 36, 48, and so on. Multiples of 15 are 15, 30, 45, 60, and the list goes on. The two numbers that are both multiples of 12 and 15 are 60 and 120. Like, easy peasy lemon squeezy!

To express 80 as the product of its prime factors, we start by dividing 80 by the smallest prime number, which is 2. 80 ÷ 2 = 40. Then, we divide 40 by 2 again to get 20. Continuing this process, we find that 80 can be expressed as 2 x 2 x 2 x 2 x 5, or 2^4 x 5.

Well, honey, the least common multiple of 64 and 7 is 448. It's the smallest multiple that both 64 and 7 can divide into evenly. So, there you have it, darling. Math can be a real hoot sometimes!

To determine if any number goes into 295 evenly, we need to find its factors. The factors of 295 are 1, 5, 59, and 295. Since 295 divided by any of these factors does not result in a whole number, 295 is not divisible by any number other than itself and 1. Therefore, no number goes into 295 evenly.

Well, honey, 334366 is divisible by 1, 2, 167, and 2002. So, if you're looking to slice and dice that number, those are your lucky options. Now go forth and conquer those divisors like the math wizard you are!

Since 54y3 is a multiple of 27y, it is automatically the LCM.

Well, honey, I hate to break it to you, but the numbers 8 and 36 are not multiples of 5. Natural numbers are those positive integers starting from 1, and multiples of 5 are numbers that can be divided by 5 without any remainder. So, in this case, you're barking up the wrong tree.

540 = 2 x 2 x 3 x 3 x 3 x 5

The factors of 136 are: 1 2 4 8 17 34 68 136 The prime factors are: 2 x 2 x 2 x 17

The Highest Common Factor (HCF) of 21 and 84 is 21. This is because 21 is a factor of both 21 and 84, and it is the largest factor that both numbers have in common. To find the HCF, you can list the factors of each number and identify the largest factor that appears in both lists.

The multiples of 47 are numbers that can be evenly divided by 47. The first few multiples of 47 are 47, 94, 141, 188, 235, and so on. To find the multiples of 47, you can simply multiply 47 by any integer (positive or negative).

It is 3 that is a common prime factor to both numbers

The GCF is 7.

(7 x 9) + (7 x 7) + (7 x 13) = 7 x 29

Write down all the factors of 108 and 252.

Hence

2)108

2)54

3)27

3)9

3)3 =

&

2)252

2)126

2)63

3)21

3)7

7)7 = 1

'2' appears in both division sets twice; 2 x 2 = 4

'3' appears in both division sets twice also 3 x 3 = 9

Hence 3 x 9 = 36 Hence '36' is the HCF.

NB The '7' and the remaining '3' are NOT common to both sets, so they cannot be part of the HCF.