Math, asked by skyspace0606, 6 hours ago

. Express 946 as a product of its Prime.​

Answers

Answered by DevTyagi123
0

Answer:

Put the given number inside the "L" shape

Step 2 :

We have to split the given number by prime numbers only. That is, always we have to put prime numbers out side the "L" shape.

Step 3 :

The tricks given below will be helpful to find the prime number which exactly divides the given number.

A number which ends with 0, 2, 4, 6 and 8 is divisible by the smallest prime number 2.

A number which ends with 0 or 5 is divisible by 5

If the sum of digits of the given number is a multiple of 3, then the given number is divisible by 3.

Step 4 :

Take the first digit of the given number and check how many times the prime number goes in to that.

Further process is explained in the examples given below.

Example 1 :

Express 324 as the product of prime factors

Solution :

Since the given number ends with 4, first we have to split the given number by the smallest prime number 2.

2 goes into 3 one time. We have 1 left. If we take this 1 along with the next digit 2, we get 12. If we divide this by 2, we get 6.

We don’t have any number remaining in 12. So we can take the next digit 4. Again, if we divide 4 by 2, we get 2.

If we repeat this process, we get

So, the prime factors of 324

= 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3

= 2234

Example 2 :

Express 625 as the product of prime factors

Solution :

Since the given number ends with 5, first we have to split it by the prime number 5.

5 goes into 6 one time. We have 1 left. If we take this 1 along with the next digit 2, we get 12. Again we have to divide it by 5. If we divide this by 5, we get 2.

Now we have 2 left. Now we have to take this 2 along with the next digit 5, we get 25. If we divide 25 by 5, we get 5.

By repeating this process until we get prime factors.

Prime factors of 625 :

= 5 ⋅ 5 ⋅ 5 ⋅ 5

= 54

Example 3 :

Express 4096 as the product of prime factors.

Solution :

Prime factors of 4096 :

= 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2

= 212

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