MGF2107 - Exploration In Mathematics Homework 5.1
Find the prime factorization of 20. Use exponents to show any repeated prime factors.
20 = 2^2x5 (2 to the power of 2, times 5).
Find the least common multiple of 152 and 380.
The least common multiple of 152 and 380 is 760.
Find the least common multiple of 84 and 24.
The least common multiple of 84 and 24 is 168.
(This question has nine parts.) Use the rules of divisibility to determine whether 41, 356 is divisible by the following numbers. ''a. 2 b. 3 c. 4 d. 5 e. 6 f. 8 g. 9 h. 10 i. 12'' a. Is 7, 323,840 divisible by 2? b. Is 7, 323,840 divisible by 3? c. Is 7, 323,840 divisible by 4? d. Is 7, 323,840 divisible by 5? e. Is 7, 323,840 divisible by 6? f. Is 7, 323,840 divisible by 8? g. Is 7, 323,840 divisible by 9? h. Is 7, 323,840 divisible by 10? i. Is 7, 323,840 divisible by 12?
a. Yes. b. Yes. c. Yes. d. Yes. e. Yes. f. Yes. g. Yes. h. Yes. i. Yes.
A relief worker needs to divide 540 bottles of water and 216 cans of foods into boxes that each contain the same number of items. Also, each box must contain the same type of item (bottled water or canned food). What is the largest number of relief supplies that can be put in each box?
108 is the largest number of supplies that can be put in each box.
Find the prime factorization of the composite number. ''255''
255 = 3x5x17.
Find the prime factorization of the composite number. ''354''
354 = 2x3x59.
Fill in the blank so that the resulting statement is true. ''A natural number greater than 1 that is divisible by a number other than itself and 1 is called a/an ____________ number.''
Composite.
Fill in the blank so that the resulting statement is true. ''The largest number that is a factor of two or more natural numbers is called their ___________________.''
Greatest Common Divisor (GCD).
Fill in the blank so that the resulting statement is true. ''The smallest number that is divisible by two or more natural numbers is called their ___________________.''
Least Common Multiple (LCM).
Determine whether the given statement is true of false, and indicate why this is so. ''3 | 5434''
No, because the sum of the digits is not divisible by 3.
Determine whether the given statement is true of false, and indicate why this is so. '' 9 | 21,732''
No, because the sum of the digits is not divisible by 9.
A perfect number is a natural number that is equal to the sum of its factors, excluding the number itself. Determine whether or not the given number is perfect. ''8''
No.
Fill in the blank so that the resulting statement is true. ''A natural number greater than 1 that has only itself and 1 as factors is called a/am ___________ number.''
Prime.
Find the greatest common divisor of 126 and 36.
The greatest common divisor of 126 and 36 is 18.
Find the greatest common divisor of 459 and 765.
The greatest common divisor of 459 and 765 is 153.
Find the least common multiple of 90 and 20.
The least common multiple of 90 and 20 is 180.
Find the prime factorization of 588.
The prime factorization is 2^2x3x7^2 (2 to the power of 2, times 3, times 7 to the power of 2).
Find the prime factorization of the following number. Write any repeated factors using exponents. ''100''
The prime factorization of 100 is 2^2 x 5^2 (2 to the power of 2 times 5 to the power of 2).
Determine whether the statement is true of false. If the statement is false, make the necessary change(s) to produce a true statement. ''The notation b|a means that b is divisible by a.''
The statement is false. The notation b|a means that a is divisible by b.
Determine whether the statement is true of false. If the statement is false, make the necessary change(s) to produce a true statement. ''A number can only be divisible by exactly one number.''
The statement is false. The true statement is ''A number is divisible by all of its factors.''
Determine whether the statement is true of false. If the statement is false, make the necessary change(s) to produce a true statement. ''The words ''factor'' and divisor'' have opposite meanings.''
The statement is false. The words ''factor'' and ''divisor'' have the same meaning.
Determine whether the statement is true of false. If the statement is false, make the necessary change(s) to produce a true statement. ''b|'a means that b does not divide a.''
The statement is true.
Determine whether the given statement is true of false, and indicate why this is so. '' 5 | 39,380''
Yes, because the last digit is not divisible by 5.
A prime number is an emirp (''prime'' spelled backward) if it becomes a different prime number when it digits are reversed. Determine whether or not the given prime number is an emirp. ''389. Is 389 an emirp?''
Yes.
You and your brother both work the 4:00 P.M. to midnight shift. You have every fourth night off. Your brother has every sixth night off. Both of you were off on August 1st. Your bother would like to see a movie with you. When will the two of you have the same night off again?
You will both have the same night off again on August 13th.
(This question has nine parts.) Use the rules of divisibility to determine whether 41, 356 is divisible by the following numbers. ''a. 2 b. 3 c. 4 d. 5 e. 6 f. 8 g. 9 h. 10 i. 12'' a. Is 41, 356 divisible by 2? b. Is 41, 356 divisible by 3? c. Is 41, 356 divisible by 4? d. Is 41, 356 divisible by 5? e. Is 41, 356 divisible by 6? f. Is 41, 356 divisible by 8? g. Is 41, 356 divisible by 9? h. Is 41, 356 divisible by 10? i. Is 41, 356 divisible by 12?
a. Yes. b. No. c. Yes. d. No. e. No. f. No. g. No. h. No. i. No.
(This question has nine parts.) Use the rules of divisibility to determine whether 9128 is divisible by the following numbers. ''a. 2 b. 3 c. 4 d. 5 e. 6 f. 8 g. 9 h. 10 i. 12'' a. Is 9128 divisible by 2? b. Is 9128 divisible by 3? c. Is 9128 divisible by 4? d. Is 9128 divisible by 5? e. Is 9128 divisible by 6? f. Is 9128 divisible by 8? g. Is 9128 divisible by 9? h. Is 9128 divisible by 10? i. Is 9128 divisible by 12?
a. Yes. b. No. c. Yes. d. No. e. No. f. Yes. g. Yes. h. No. i. No.
Determine all values of d that makes the statement true. ''4 | 83734d''
d = 0,4,8.
