Factors Of 15 In Pairs

Factors of 91 are those numbers that divide the number 91 completely without any remainder. In that location are four factors of 91 which are i, 7, 13, and 91. 1 is the smallest gene of 91 while 91 itself is the largest cistron of 91. When two numbers are multiplied in pair with each other and give the value as 91, then that set of numbers is called the pair factor of 91. The factors of 91 in pairs are (1, 91) and (7, xiii). The prime factorization of 91 is 7 10 13 with 7 and thirteen as the two prime factors of 91.

Key Terms: Factors of 91, Prime Factorization, Prime number Factors, Pair Factor, Partitioning, Remainder, Whole Number, Remainder

What are Factors of 91?

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Factors of 91 are the numbers that divide 91 exactly leaving the remainder equally zilch. Information technology ways on partitioning with 91, the factors of 91 give the quotient in the form of a whole number and not in fractions or decimals. ane, 7, thirteen, and 91 are the 4 factors of 91.

Factors of 91: ane, vii, xiii, 91

Factors of 91

Factors of 91

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How to Summate Factors of 91?

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Factors of 91 can exist calculated using two methods namely:

Prime Factorization
Division Method

In the prime number factorization of 91, 91 is expressed as the production of its prime number factors. Through division methods, nosotros check what numbers divide 91 exactly without a residuum.

Read More than: Co Prime number Numbers

Factors of 91 By Partitioning Method

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In gild to bank check the factors of 91, we will divide 91 by all the numbers from 1 to 91. If the number divides 91 completely and zero is left as the remainder, then, that means that number is a gene of 91.

The factors of 91 by division method are as follows:

91 ÷ 91 = 1
91 ÷ vii = xiii

Thus, 1, 7, 13, and 91 are the iv factors of 91. Any other number apart from these four numbers would not divide 91 completely, i.e will leave the balance at the cease.

Prime Factorization of 91

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91 is a composite number which means that it must have prime factors.

Prime Factorization of 91

Prime number Factorization of 91

Stride 1: Divide the number 91 by the smallest prime number factor, say 7.

91 ÷ 7 = 13

Step 2: When we split up 13 past 7, we will get a fraction, which means that it cannot exist a factor of a number.

Footstep 3: Nosotros will now continue with the adjacent prime factor, say 13.

13 ÷ 13 = 1

We have received the number 1 at the end of the division process, i.eastward. nosotros cannot proceed further. Thus, the prime factorization of 91 is written every bit 7 x xiii, where 7 and 13 are the prime numbers.

Read More: Prime number Number Formula

Factors of 91 in Pairs

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Ii numbers that, when multiplied together, give 91 as the product are known as the pair factors of 91. We can see that,

1 x 91 = 91
13 x 7 = 91

Thus, the factors of 91 in pairs are (one, 91) and (7, 13).

The pair factors of a number tin be negative also since the product of ii negative numbers is positive.

-1 10 -91 = 91
-13 x -vii = 91

The negative factor pairs of 91 are (-1, -91) and (-7, -13).

Read More: Twin Primes

Solved Examples on Factors of 91

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Example ane: There are 13 members in a hall and each of them has 7 books. Calculate how many total books are at that place in the hall.

Solution: Information technology is given that,

Number of Members = 13
Number of Books with each member = 7
Total Number of Books in the Hall = 13 10 7 = 91

Thus, at that place are a total of 91 books in the hall.

Case 2: Listing the common factors of 91 and 126.

Solution: Writing down all the factors of 91 and 126,

Factors of 91: 1, 7, 13, and 91.
Factors of 126: 1, 2, 3, 6, vii, 9, 14, 18, 21, 42, 63, and 126.

Thus, 1 and 7 are the only common factors of 91 and 126.

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Things to Think

Factors of 91 are the whole numbers that split 91 completely without leaving whatsoever residuum.
In that location are four factors of 91.
1, 7, 13, and 91 are the four factors of 91.
The prime factorization of 91 is seven x xiii.
The sum of all the factors of 91 is 112.
The factors of 91 in pairs are (1, 91) and (vii, thirteen).

Sample Questions

Ques. Anita wants to list the factors of 91 and find the positive pair factors. Assistance her with the same. (2 Marks)

Ans. The factors of 91 are the numbers that divide 91 exactly without leaving any residuum. The factors of 91 are one, vii, 13, and 91.

Pair factors of 91 are the pairs of two numbers that requite 91 as the product on multiplication with each other.

1 × 91 = 91
vii × 13 = 91
xiii × vii = 91
91 × one = 91

Thus, the pair factors of 91 are (1, 91) and (7, thirteen).

Ques. Notice out the number which on multiplying with (-7) gives 91. (2 Marks)

Ans. In guild to observe out the number that gives 91 on multiplying with (-7), we need to divide 91 past -7

91 ÷ -7 = -thirteen

Thus, -xiii on multiplying with -7 gives 91.

Ques. What is the product of all the prime factors of 91? (2 Marks)

Ans. The prime number factors of 91 are the numbers that divide 91 completely and are prime in nature. The two prime factors of 91 are seven, and xiii. Thus, the product of prime number factors will exist

vii × 13 = 91

Ques. Name the greatest common factor of 91 and 27. (two Marks)

Ans. Listing all the factors of 91 and 27, nosotros get

Factors of 91: ane, 7, 13, 91
Factors of 27: 1, 3, 9, 27.

Thus, 91 and 27 have simply ane common factor which is 1 which implies that 91 and 27 are co-prime. The Greatest Common Gene (GCF) of 91 and 27 is 1.

Ques. Notice out the sum of the factors of 91. (2 Marks)

Ans. The factors of 91 are 1, 7, 13, and 91.

Adding upwardly all of these factors, nosotros become

1 + 7 + 13 + 91 = 112

Thus, the sum of all the factors of 91 is 112.

Ques. What are the common factors of 11 and 91? (2 Marks)

Ans. The factors of 11 and 91 are:

Factors of 91 are 1, vii, thirteen, and 91.
Factors of 11 are ane, and 11.

Thus, 91 and 11 have simply one mutual cistron which is one which means that 91 and 11 are co-prime.

Ques. Are the multiples and factors of 91 the aforementioned thing? (two Marks)

Ans. No, multiples and factors of 91 are two different concepts.

Factors of 91 are the numbers that divide 91 completely leaving zip every bit the residual. Factors of 91 are 1, 7, 13, and 91.
Multiples of 91 are the numbers obtained when 91 is multiplied by any number. The multiples of 91 are 91, 182, 273, 364, 455, 546, 637, 728, 819, and 910.

Ques. What are the multiples of 91? (ii Marks)

Ans. The multiples of 91 are the products obtained when 91 is multiplied past an integer. The multiples of 91 are infinite which means that the multiples of 91 are never-ending.

91 × ane = 91
91 × two = 182
91 × 3 = 273
91 × 4 = 364
91 × 5 = 455
91 × half-dozen = 546
91 × seven = 637
91 × viii = 728
91 × 9 = 819
91 × 10 = 910

Ques. Name the 2nd greatest number cistron of 91. (1 Marking)

Ans. There are four factors of 91 which are 1, vii, 13, and 91 of which the 2nd greatest gene of 91 is 13.

Ques. Summate the sum and average of the get-go ten multiples of 91. (2 Marks)

Ans. We know that the first 10 multiples of 91 are 91, 182, 273, 364, 455, 546, 637, 728, 819, and 910. Thus,

Sum of offset 10 Multiples: 91 + 182 + 273 + 364 + 455 + 546 + 637 + 728 + 819 + 910 = 5005
Boilerplate of first 10 Multiples: Sum of start 10 Multiples of 91/x = (5005) /ten = 500.five

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