How to use the QUOTIENT function

The quotient function returns the integer portion of a division. The remainder is left out. This function is useful in scenarios where you need only the whole number result of a division, ignoring any fractional part.

Example, 5/2 = 2.5. The integer is 2. The remainder is 0.5

1. Introduction

What is an integer?

An integer is a whole number that can be positive, negative, or zero, but not a fraction or decimal.

What is a whole number?

A whole number is a number without any fractional or decimal parts. Whole numbers are the set of non-negative integers. Examples: 0, 1, 2, 3, 4, 5, and so on.

Whole numbers are used for counting discrete objects and in many basic mathematical operations. While whole numbers include only non-negative integers, the set of integers includes negative numbers as well.

What is a remainder?

A remainder is what's left over after division when one number doesn't divide evenly into another. The amount left over when one number cannot be divided evenly by another.

In the division 17 ÷ 5 The quotient is 3. The remainder is 2 (Because 5 goes into 17 three times with 2 left over)

What is division?

Division in mathematics is one of the four basic arithmetic operations, alongside addition, subtraction, and multiplication. Division is the process of splitting a quantity into equal parts or groups.

Components:

• Dividend: The number being divided
• Divisor: The number dividing the dividend
• Quotient: The result of the division
• Remainder: The amount left over (if division isn't exact)

Example:

• In 20 ÷ 4 = 5
• 20 is the dividend
• 4 is the divisor
• 5 is the quotient

Types:

• Exact division: No remainder (e.g., 12 ÷ 3 = 4)
• Non-exact division: Has a remainder (e.g., 14 ÷ 3 = 4 remainder 2)

2. Syntax

QUOTIENT(numerator, denominator)

numerator	Required. The dividend.
denominator	Required. The divisor.

The QUOTIENT function returns the #VALUE! if the arguments are not numbers.

The following formula is equivalent to the QUOTIENT function:

3. Example 1

The first example uses 10 as the numerator and 3 as the denominator located in cells B3 and C3 respectively. The QUOTIENT function output in cell E3 is 3.

Formula in cell E3:

Lets do some manual calculations, what is the integer part of 10 divided by 3?
10 / 3 = 3.333333 The integer part is 3.
3 * 3 = 9
10 - 9 = 1 The remainder is 1.

The second example uses 5 as the numerator and 2 as the denominator located in cells B4 and C4 respectively. The QUOTIENT function output in cell E4 is 2.

Formula in cell E4:

Lets do some manual calculations, what is the integer part of 5 divided by 2?
5 / 2 = 2.5  The integer part is 2.
2 * 2 = 5
5 - 4 = 1 The remainder is 1.

The third example uses 48 as the numerator and 9 as the denominator located in cells B5 and C5 respectively. The QUOTIENT function output in cell E5 is 5.

Formula in cell E5:

Lets do some manual calculations, what is the integer part of 48 divided by 9?
48 / 9 = 5  The integer part is 5.
9 * 5 = 45
48 - 45 = 3 The remainder is 3.

4. Example 2

You're preparing to ship your company's products to customers. You have:

1. 18 units of product A in stock (stored in cell B2)
2. Shipping boxes that can each hold 4 units of product A (capacity stored in cell C2)

How many boxes will you need to package product A for shipping if  all boxes needs to be full?

QUOTIENT(numerator, denominator)

There are two arguments, the numerator is the dividend and the denominator is the divisor.

The formula in cell D2:

returns 4. This means that you need 4 boxes to ship 16 products. 2 products remains.

If you divide 18 by 4, you get 4.5.

The Quotient function returns 4 because the integer part of 4.5 is 4.

Back to top

5. Example 3

How to find divisors of a number that return no remainders?

The formula in cell C4 shown in the image above is a dynamic array formula that automatically spills values to cells below. It calculates all divisors that can be used so the result returns a whole number based on the dividend specified in cell C2.

Example, number 5 returns no remainders. 100/5 = 20. The result is a whole number. Change the number in cell C2 and Excel automatically calculates divisors in cell C4 and cells below. There is a dividend limit of 1048576, you can't go higher than that.

Excel 365 formula in cell C4:

The following formula is an array formula, it works for all previous Excel versions and returns the same numbers as the Excel 365 formula.

Array formula for previous Excel versions:

How to enter an array formula

1. Double press with left mouse button on with left mouse button on cell C4.
2. Paste the formula.
3. Press and hold CTRL + SHIFT keys simultaneously.
4. Press Enter once.
5. Release all keys.

Copy cell C4 and paste to cells below as far as needed. This is required if you are using the array formula.

Explaining Excel 365 formula in cell C4

Step 1 - Create a sequence

The SEQUENCE function returns an array containing a sequence of numbers.

SEQUENCE(C2)

becomes

SEQUENCE(100)

and returns {1; 2; 3; ... 98; 99; 100}. Not all numbers are shown in this sequence.

Step 2 - Calculate remainders

The MOD function returns the remainder of a division.

MOD($C$2,SEQUENCE($C$2))

becomes

MOD(100, {1; 2; 3; ... 98; 99; 100})

and returns {0 ;0 ;1 ; ... ; 2; 1; 0}.

Step 3 - Create a logical expression

The equal sign allows you to compare the numbers in the array to 0 (zero). The result is boolean values TRUE or FALSE.

MOD(C2,SEQUENCE(C2))=0

becomes

{0 ;0 ;1 ; ... ; 2; 1; 0}=0

and returns {TRUE ;TRUE ;FALSE; ... ; FALSE; FALSE; TRUE }.

Step 4 - Filter values based on logical expression

The FILTER function lets you extract values/rows based on a condition or criteria.

FILTER(SEQUENCE(C2), MOD(C2,SEQUENCE(C2))=0)

becomes

FILTER(SEQUENCE(C2), {TRUE ;TRUE ;FALSE; ... ; FALSE; FALSE; TRUE })

becomes

FILTER({1; 2; 3; ... 98; 99; 100}, {TRUE ;TRUE ;FALSE; ... ; FALSE; FALSE; TRUE })

and returns {1; 2; 4; 5; 10; 20; 25; 50; 100}.

Back to top

6. Example 4

The image above demonstrates a formula that returns repeating numbers in a sequence. For example, 0, 0, 0, 1, 1, 1, 2, 2, 2 etc.

The second argument determines how many times a number is repeated before moving on to the next number.

Formula in cell B3:

Change the formula to this if you want the sequence to start with 1 instead of 0 (zero).

Explaining formula in cell B3

Step 1 - Calculate a number that changes based on a relative and absolute cell ref

The ROWS function returns a number representing the number of rows in cell reference. Cell ref $A$1:A1 is a growing cell reference that changes when you copy the cell and paste to cells below.

It contains an absolute ($A$1) indicated by the dollar signs and a relative part (A1).

ROWS($A$1:A1)-1

becomes

1-1

amd returns 0 (zero).

Step 2 - Calculate quotient

QUOTIENT(numerator, denominator)

QUOTIENT(ROWS($A$1:A1)-1,3)

becomes

QUOTIENT(0,3)

and returns 0 (zero) in cell B3.

Back to top

Back to top

Useful links

QUOTIENT function  - Microsoft
QUOTIENT

'QUOTIENT' function examples

Functions in 'Math and trigonometry' category

The QUOTIENT function function is one of 61 functions in the 'Math and trigonometry' category.

Excel function categories

Excel categories

Comments (3)