In most states, if not all states, six is the cut off when it comes to the need for child care. Thus six years old have been ruled old enough by State Welfare Agencies to be on their own.
Colorado is a state that retains the Common Law Marriage concept. The courts have indicated that they will follow a Pennsylvania Supreme Court case as to what age can a person enter into a Common Law Marriage (The ruling is from the late 1990s and it held that age was 12). Since Colorado have NOT forbade people under 12 from entering into a Common Law Marriage, and 12 was the age of consent under the Common Law, it is still the age in Colorado. Please note, Pennsylvania like Colorado had made it illegal enter into a ceremonial marriage (one that requires a marriage license) who was NOT 18 years of age, but nothing is such statute affects Common Law Marriages.
Please also note, while Common Law Marriages require no state act (i.e, no need for a license) they are valid marriages and can only be ended by a Divorce or annulment.
You are lucky, Colorado Welfare regs actually uses age 13:
3.902 CHILD CARE PROGRAM ELIGIBILITY
"Eligible child" means a child under the age of thirteen (13) years who needs child care services during a portion of the day, but less than 24 hours, and is physically residing with the eligible adult caretaker(s) during the same period care is needed; or a child under age nineteen (19) who is physically or mentally incapable of caring for himself or herself or is under court supervision. Any child served through the Colorado Works Program or the Low-Income Child Care Program must be a citizen of the United States or a qualified alien as defined in Section 3.919, H, 1.
http://stateboard.cdhs.state.co.us:8008/CDHS/rule_display$.DisplayVolume?p_vol_num=3
You are lucky that your state actually uses age 13 as a cut off but notice only if that who needs child care services .... If the child can be left alone at a young age, no child care is provided. This is the MAXIMUM age some one can get child care for NOT the minimum age.
As to the age to be left alone the Colorado Department of Human Services says the following:
The laws of Colorado do not set a specific age after which a child legally can stay home alone. Unfortunately, age is not a very good indicator of a child's maturity level. Some 15- year-olds may still not be ready. For example, it is inappropriate to leave a 15-year-old alone if the teen is chemically dependent, has emotional problems, or is prone to vandalism or other destructive or illegal acts.
Colorado in general has accepted the age of 12 years as a guideline for when it might be appropriate for a child to be left alone for short periods of time. This standard is based upon the Colorado Child Labor Law, which deems 12 years as the minimum age for employment, for example a babysitter. (See Colorado Revised Statutes. § 8-12-105 (3) ).
http://www.cdhs.state.co.us/childwelfare/LeaveKidsAlone.htm
Colorado generally uses 14 as the age cutoff but under 8-12-106, nine years old and twelve years old can do the following jobs:
8-12-106. Permissible occupations at age nine or older.
(1) Subject to the limitations of sections 8-12-105 and 8-12-110, any minor at age nine or older shall be permitted employment in any of the following nonhazardous occupations:
(a) Delivery of handbills, advertising, and advertising samples;
(b) Shoeshining;
(c) Gardening and care of lawns involving no power-driven lawn equipment;
(d) Cleaning of walks involving no power-driven snow-removal equipment;
(e) Casual work usual to the home of the employer and not specifically prohibited in this article;
(f) Caddying on golf courses;
(g) Any other occupation which is similar to those enumerated in this subsection (1) and is not specifically prohibited by this article.
8-12-107. Permissible occupations at age twelve or older.
(1) Subject to the limitations of sections 8-12-105 and 8-12-110, any minor at age twelve or older shall be permitted employment in any of the following nonhazardous occupations:
(a) Sale and delivery of periodicals and door-to-door selling of merchandise and the delivery thereof;
(b) Baby-sitting;
(c) Gardening and care of lawns, including the operation of power-driven lawn equipment if such type of equipment is approved by the division or if the minor has received training conducted or approved by the division in the operation of the equipment;
(d) Cleaning of walks, including the operation of power-driven snow-removal equipment;
(e) Agricultural work, except for that declared to be hazardous under the "Fair Labor Standards Act of 1938", as amended. However, it is the intent of the general assembly that migrant children eligible for attendance at migrant schools be encouraged to attend such schools.
(f) Any other occupation which is similar to those enumerated in this subsection (1) and is not specifically prohibited by this article.