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Is 77 a multiply of 3?
231
What is a factorization for 231?
Factorizations for 231 are: 1) 231 = 1x231 2) 231 = 3x7x11 3) 231 = 21x11 4) 231 = 3x77 5) 231 = 33x7
What two numbers do you multiply to get 231?
1 x 231, 3 x 77, 21 x 11, 33 x 7. Add the digits and you get 6, which means it is divisible by 3. (3 x 77) 77 has two prime factors, 7 and 11. So you can multiply any combination of the factors to get 231. 3C2 (3 choose 2) in Pascal's triangle is 3, which means there are three possible combinations. Oh, yeah, and you can always just do 1 x 231.
What goes into 231?
To determine factors of a number it is necessary to divide the number by prime numbers of increasing value. If there is no remainder then the prime number is a factor. The square root of 231 is approximately 15 so it is necessary to divide by all the prime numbers up to 13 (15 is not a prime number). 231 ÷ 2 leaves a remainder of 1 231 ÷ 3 divides exactly 77 times (which is 7 x 11 - both are prime numbers) 231 ÷ 5 leaves a remainder of 1 231 ÷ 7 divides exactly 33 times (which is 3 x 11 - both are prime numbers) 231 ÷ 11 divides exactly 21 times (which is 3 x 7 - both are prime numbers) 231 ÷ 13 leaves a remainder of 10 If we multiply together the three numbers that are shown to be factors 3 x 7 x 11 = 231 this confirms that there are no other factors of 231 except 1 and 231 itself. This last condition is true for every positive integer. 231 is divisible by 1, 3, 7, 11 and 231
How many numbers between 100 and 300 are divisible by 11?
There are 18 numbers between 100 and 300 that are divisible by 11: 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297.
