# What is GCF of 35 and 63?

GCF of 35 and 63 is 7

#### How to find GCF of two numbers

 1.   Steps to find GCF of 35 and 63 2.   What is GCF of two numbers? 3.   What are Factors? 4.   Examples of GCF

### Example: Find gcf of 35 and 63

• Factors for 35: 1, 5, 7, 35
• Factors for 63: 1, 3, 7, 9, 21, 63

Hence, GCf of 35 and 63 is 7

#### Definition of GCF

Greatest common factor commonly known as GCF of the two numbers is the highest possible number which completely divides given numbers, i.e. without leaving any remainder. It is represented as GCF (35, 63).

#### Properties of GCF

• The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.
• GCF of two consecutive numbers is always 1.
• Given two numbers 35 and 63, such that GCF is 7 where 7 will always be less than 35 and 63.
• Product of two numbers is always equal to the product of their GCF and LCM.

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of Factors

• Every number is a factor of zero (0), since 35 x 0 = 0 and 63 x 0 = 0.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 5, 7, 35 are exact divisors of 35 and 1, 3, 7, 9, 21, 63 are exact divisors of 63.
• Factors of 35 are 1, 5, 7, 35. Each factor divides 35 without leaving a remainder.
Simlarly, factors of 63 are 1, 3, 7, 9, 21, 63. Each factor divides 63 without leaving a remainder.

#### Steps to find Factors of 35 and 63

• Step 1. Find all the numbers that would divide 35 and 63 without leaving any remainder. Starting with the number 1 upto 17 (half of 35) and 1 upto 31 (half of 63). The number 1 and the number itself are always factors of the given number.
35 ÷ 1 : Remainder = 0
63 ÷ 1 : Remainder = 0
35 ÷ 5 : Remainder = 0
63 ÷ 3 : Remainder = 0
35 ÷ 7 : Remainder = 0
63 ÷ 7 : Remainder = 0
35 ÷ 35 : Remainder = 0
63 ÷ 9 : Remainder = 0
63 ÷ 21 : Remainder = 0
63 ÷ 63 : Remainder = 0

Hence, Factors of 35 are 1, 5, 7, and 35

And, Factors of 63 are 1, 3, 7, 9, 21, and 63

#### Examples of GCF

Sammy baked 35 chocolate cookies and 63 fruit and nut cookies to package in plastic containers for her friends at college. She wants to divide the cookies into identical boxes so that each box has the same number of each kind of cookies. She wishes that each box should have greatest number of cookies possible, how many plastic boxes does she need?

Since Sammy wants to pack greatest number of cookies possible. So for calculating total number of boxes required we need to calculate the GCF of 35 and 63.
GCF of 35 and 63 is 7.

A class has 35 boys and 63 girls. A choir teacher wants to form a choir team from this class such that the students are standing in equal rows also girls or boys will be in each row. Teacher wants to know the greatest number of students that could be in each row, can you help him?

To find the greatest number of students that could be in each row, we need to find the GCF of 35 and 63. Hence, GCF of 35 and 63 is 7.

What is the difference between GCF and LCM?

Major and simple difference betwen GCF and LCM is that GCF gives you the greatest common factor while LCM finds out the least common factor possible for the given numbers.

What is the relation between LCM and GCF (Greatest Common Factor)?

GCF and LCM of two numbers can be related as GCF(35, 63) = ( 35 * 63 ) / LCM(35, 63) = 7.

What is the GCF of 35 and 63?

GCF of 35 and 63 is 7.

Ariel is making ready to eat meals to share with friends. She has 35 bottles of water and 63 cans of food, which she would like to distribute equally, with no left overs. What is the greatest number of boxes Ariel can make?

The greatest number of boxes Ariel can make would be equal to GCF of 35 and 63. So the GCF of 35 and 63 is 7.

Mary has 35 blue buttons and 63 white buttons. She wants to place them in identical groups without any buttons left, in the greatest way possible. Can you help Mary arranging them in groups?

Greatest possible way in which Mary can arrange them in groups would be GCF of 35 and 63. Hence, the GCF of 35 and 63 or the greatest arrangement is 7.

Kamal is making identical balloon arrangements for a party. He has 35 maroon balloons, and 63 orange balloons. He wants each arrangement tohave the same number of each color. What is the greatest number of arrangements that he can make if every balloon is used?

The greatest number of arrangements that he can make if every balloon is used would be equal to GCF of 35 and 63. So the GCF of 35 and 63 is 7.

Kunal is making baskets full of nuts and dried fruits. He has 35 bags of nuts and 63 bags of dried fruits. He wants each basket to be identical, containing the same combination of bags of nuts and bags of driesn fruits, with no left overs. What is the greatest number of baskets that Kunal can make?

the greatest number of baskets that Kunal can make would be equal to GCF of 35 and 63. So the GCF of 35 and 63 is 7.

A class has 35 boys and 63 girls. A choir teacher wants to form a choir team from this class such that the students are standing in equal rows also girls or boys will be in each row. Teacher wants to know the greatest number of students that could be in each row, can you help him?

To find the greatest number of students that could be in each row, we need to find the GCF of 35 and 63. Hence, GCF of 35 and 63 is 7.

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