A "whole" number is an integer. The whole numbers are ...-3,-2,-1,0,1,2,3,... "Divided into two" here means "written as the sum of two". Even numbers can be written as the sum of two equal integers, for example 18 is even and we can write 18 = 9 + 9. -70 is even (minus seventy) and we can write -70 = (-35)+(-35). Zero is even and we can write 0 = 0+0. No, the sentence is not true without the part marked in stars. 7 is not even but you can write 7=2+5 as the sum of two numbers which, however, are not equal.

In mathematics, the word "number" includes many different sets of numbers, including the natural numbers (1, 2, 3, 4, 5), the integers (-3, -2, -1, 0, 1, 2, 3), the fractions, (1/3, 22/7, etc.), the real numbers (√2, π), the imaginary numbers (2i, -3.5i), the complex numbers (1 + 2i, 26.583 - 8.791i), and I think others. So 3.5, for example, is "a number." The phrase "whole number" means the same thing as "integer." The word "whole" is needed. 7 is not an even number. However, it can be divided into two equal numbers, 3.5 and 3.5, but they are not "whole numbers." The word "equal" is needed. 7 is not an even number. However, it can be divided into two whole numbers, 2 and 5. 2 and 5 are whole numbers, but they are not equal numbers. In mathematics, some words have meanings that are different from their everyday meanings. And, in mathematics, some words have meanings that are more carefully defined than in everyday life. Mathematics has its own specialized vocabulary. If the phrase is in a textbook, check to see if there is a glossary in the back. If so, it will give the meanings of the words used in the textbook, in the way in which the textbook uses them.

P.S. The phrase "divided into..." tells us that we aren't talking about the mathematical operation of division. You could rewrite the sentence, correctly, using the phrase "divided by two," in a several ways. "An even number is a number that can be divided by two with no remainder." You could also say "An even number is a number that is an exact multiple of 2."