What is GCF of 49 and 343?

Go back to 'All gcf of pages' >

GCF of 49 and 343 is 49

How to find GCF of two numbers

Steps to find GCF of 49 and 343

Find all the numbers that would divide 49 and 343 without leaving any remainder as explained in factors below.
Find the greatest common factor from the list of factors for 49 and 343, and read off the answer!

Example: Find gcf of 49 and 343

Factors for 49: 1, 7, 49
Factors for 343: 1, 7, 49, 343

Hence, GCf of 49 and 343 is 49

How do you explain GCF in mathematics?

GCF or greatest common factor of two or more numbers is defined as largest possible number or integer which is the factor of all given number or in other words we can say that largest possible common number which completely divides the given numbers. GCF of two numbers can be represented as GCF (49, 343).

Properties of GCF

The GCF of two or more given numbers is always less than the given numbers. Eg- GCF of 49 and 343 is 49, where 49 is less than both the numbers.
If the given numbers are consecutive than GCF is always 1.
Product of two numbers is always equal to the product of their GCF and LCM.
The GCF of two given numbers where one of them is a prime number is either 1 or the number itself.

How can we define factors?

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

Properties of Factors

Every factor of a number is an exact divisor of that number, example 1, 7, 49 are exact divisors of 49 and 1, 7, 49, 343 are exact divisors of 343.
Every number other than 1 has at least two factors, namely the number itself and 1.
Each number is a factor of itself. Eg. 49 and 343 are factors of themselves respectively.
1 is a factor of every number. Eg. 1 is a factor of 49 and also of 343.

Steps to find Factors of 49 and 343

Step 1. Find all the numbers that would divide 49 and 343 without leaving any remainder. Starting with the number 1 upto 24 (half of 49) and 1 upto 171 (half of 343). The number 1 and the number itself are always factors of the given number.

49 ÷ 1 : Remainder = 0

343 ÷ 1 : Remainder = 0

49 ÷ 7 : Remainder = 0

343 ÷ 7 : Remainder = 0

49 ÷ 49 : Remainder = 0

343 ÷ 49 : Remainder = 0

343 ÷ 343 : Remainder = 0

Hence, Factors of 49 are 1, 7, and 49

And, Factors of 343 are 1, 7, 49, and 343

Examples of GCF

Sammy baked 49 chocolate cookies and 343 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 49 and 343.
GCF of 49 and 343 is 49.

A class has 49 boys and 343 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 49 and 343. Hence, GCF of 49 and 343 is 49.

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(49, 343) = ( 49 * 343 ) / LCM(49, 343) = 49.

What is the GCF of 49 and 343?

GCF of 49 and 343 is 49.

Mary has 49 blue buttons and 343 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 49 and 343. Hence, the GCF of 49 and 343 or the greatest arrangement is 49.

Kamal is making identical balloon arrangements for a party. He has 49 maroon balloons, and 343 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 49 and 343. So the GCF of 49 and 343 is 49.

Kunal is making baskets full of nuts and dried fruits. He has 49 bags of nuts and 343 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 49 and 343. So the GCF of 49 and 343 is 49.

To energize public transportation, Abir needs to give a few companions envelopes with transport tickets, and metro tickets in them. On the off chance that he has 49 bus tickets and 343 metro tickets to be parted similarly among the envelopes, and he need no tickets left. What is the greatest number of envelopes Abir can make?

To make the greatest number of envelopes Abir needs to find out the GCF of 49 and 343. Hence, GCF of 49 and 343 is 49.