Question

Check whether 864 is divisible by 36? Verify whether 864 is divisible by all the factors of 36?

Answer 1

Hint: A factor is a number that divides into another number exactly and without leaving a
remainder. Most numbers have an even number of factors; however, a square number has an odd number of factors. A prime number has only two factors - the number itself and 1. The quickest way to find the factors of a number is to divide it by the smallest prime number (bigger than 1) that goes into it evenly with no remainder. Continue this process with each number we get, until we reach 1.

Complete step-by-step answer:
Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number, we get the original number. For example, 1,2,3,6 are the factors of 6. On multiplying two or more numbers we get 6.
First, we have to break 36 into factors 9 and 4 and
Now, we have to check simultaneously both the conditions of divisibility by 4 and 9
(i) for divisible by 4, The last two digit should be divisible by 4
(ii) for divisible by 9, the sum of all digits must be divisible by 9
So, as we can see
(i)satisfying 864 and $8+6+4=18$ hence,
(ii) also satisfying 864
Therefore 864 is divisible by 36.
All factors of $36=2 \times 3 \times 2 \times 3$
Divisibility Rule of 2 is the number should be even.
Divisibility Rule of 3 is the sum of digits must be divisible by 3
Now,864 is even and $8+6+4=18$
Hence, 864 is divisible by 2,3

Note: In Mathematics, factorisation or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc. Factoring is a common mathematical process used to break down the factors, or numbers, that multiply together to form another number. Factoring is useful in resolving various numbers related problems. We say that a polynomial is factored completely when we can't factor it any more. Here are some suggestions that we should follow to make sure that we factor completely: Factor all common monomials first. Identify special products such as the difference of squares or the square of a binomial.