what is the prime factorization of 210

Video What is the prime product of 210? Did you know 210 is the only number that is divisible by all numbers from 1 to 7 (minus 4) without leaving a remainder? Try it yourself. In fact, you may have discovered that if you multiply three consecutive numbers 5, 6 and 7, it will also give you 210! In this lesson, we will calculate the factor of 210, prime factor of 210 and factor of 210 in pairs along with solved examples for your better understanding.

• Elements of 210: 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105 and 210
• Prime factors of 210: 210 = 2 × 3 × 5 × 7

1. What is the factor of 210? 2. How to calculate the factors of 210? 3. Factors of 210 by prime factors 4. Factors of 210 in pairs 5. Important Notes 6. Frequently asked questions about Factor of 210

What are the factors of 210?

The factors of 210 will be the numbers that exactly divide it and give a remainder of 0. For example, when you multiply any two integers and get 210, you can say that the two numbers will be factor of 210. For example, you can take 210 as the result for: Reading: what is the prime factor of 210

• 1 × 210 = 210
• 2 × 105 = 210
• 3 × 70 = 210
• 5 × 42 = 210
• 6 × 35 = 210
• 7 × 30 = 210
• 10 × 21 = 210
• 14 × 15 = 210

This can be continued until you reach 210 × 1 = 210. So, in general, we can say that a factor of 210 is all the integers that 210 can divide.

How to calculate the factors of 210?

Let’s start calculating the factors of 210, starting with the smallest integer ie 1. Divide 210 by this number. Is the remainder 0? Right! So we will get:

• 210 1 = 210
• 210 × 1 = 210

Next integer is 2. Now divide 210 by this number.

• 210 2 = 105
• 2 × 105 = 210

Read more: What is the prime factor of 48 Proceed in the same way that we get,

• 1 × 210 = 210
• 2 × 105 = 210
• 3 × 70 = 210
• 5 × 42 = 210

Explore elements using interactive illustrations and examples

• Factories of 121 – The factors of 121 are 1, 11 and 121.
• Factories of 125 – The factors of 125 are 1, 5, 25, and 125.
• Factories of 128 – The factors of 128 are 1, 2, 4, 8, 16, 32, 64, and 128.
• The coefficients of 112 – The coefficients of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56 and 112.
• The coefficients of 512 – The coefficients of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256 and 512.
• Factors of 20 – The factors of 1, 2, 4, 5, 10 and 20.

The factors of 210 in prime factors

Prime factor means to denote a number that is the product of its prime factors. To get the prime factor of 210, we will divide it by its smallest prime factor of 2. Now, 105 is divided by the smallest prime factor and the quotient is obtained. This process continues until we get a quotient of 1. The prime factorization of 210 is shown below.Read more: 60 centimeters in inches Now that we’ve done the prime factoring of a number, we can multiply the numbers and get other factors of 210. You can try and find out if it’s all Are the factors covered? And as you may have guessed, for prime numbers, there are no other factors.

Elements of 210 in pairs

Pairs that give 210 when multiplied are called powers of 210. The following pairs of numbers are factors of 210 in pairs: Product form 210 Pair element 1 × 210 = 210 × 1 = 210 (1,210) 2 × 105 = 105 × 2 = 210 (2,105) 3 × 70 = 70 × 3 = 210 (3,70) 5 × 42 = 42 × 5 = 210 (5,42) 6 × 35 = 35 × 6 = 210 (6,35) 7 × 30 = 30 × 7 = 210 (7,30) 10 × 21 = 21 × 10 = 210 (10,21) 14 × 15 = 15 × 14 = 210 (14,15)Observe in the table above, that after 14 × 15, the elements start repeating, except that they are in a different order. So it is enough to find the elements until (14,15).

• If we consider negative integers, then both numbers in the factor pair must be negative.
• We know that – ve (×) – ve = + ve.
• Therefore, we can have 210 factor pairs as (-1, -210); (-2, -105); (-3, -70). and such.

Important note:

• The coefficients of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, and 210.
• 1 is a universal element.
• Two numbers are multiplied together to give a product that is a factor of the product.
• Since 210 ends with the digit 0, it will have 5 and 10 as its factors. This is true for any number ending with the digit 0.
• 210 is an imperfect squared number. As such, it will have an even number of elements. This property holds for all imperfect squares.

Think Tanks:Read more: What is the weight of a typical tank agitator

• Are 0.1 and 2100 a factor of 210? Why you think so?

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