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 (375, 492).
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 375 and 492, such that GCF is 3 where 3 will always be less than 375 and 492.
- 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 375 x 0 = 0 and 492 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, 3, 5, 15, 25, 75, 125, 375 are exact divisors of 375 and 1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 246, 492 are exact divisors of 492.
- Factors of 375 are 1, 3, 5, 15, 25, 75, 125, 375. Each factor divides 375 without leaving a remainder.
Simlarly, factors of 492 are 1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 246, 492. Each factor divides 492 without leaving a remainder.
Steps to find Factors of 375 and 492
- Step 1. Find all the numbers that would divide 375 and 492 without leaving any remainder. Starting with the number 1 upto 187 (half of 375) and 1 upto 246 (half of 492). The number 1 and the number itself are always factors of the given number.
375 ÷ 1 : Remainder = 0
492 ÷ 1 : Remainder = 0
375 ÷ 3 : Remainder = 0
492 ÷ 2 : Remainder = 0
375 ÷ 5 : Remainder = 0
492 ÷ 3 : Remainder = 0
375 ÷ 15 : Remainder = 0
492 ÷ 4 : Remainder = 0
375 ÷ 25 : Remainder = 0
492 ÷ 6 : Remainder = 0
375 ÷ 75 : Remainder = 0
492 ÷ 12 : Remainder = 0
375 ÷ 125 : Remainder = 0
492 ÷ 41 : Remainder = 0
375 ÷ 375 : Remainder = 0
492 ÷ 82 : Remainder = 0
492 ÷ 123 : Remainder = 0
492 ÷ 164 : Remainder = 0
492 ÷ 246 : Remainder = 0
492 ÷ 492 : Remainder = 0
Hence, Factors of
375 are 1, 3, 5, 15, 25, 75, 125, and 375
And, Factors of
492 are 1, 2, 3, 4, 6, 12, 41, 82, 123, 164, 246, and 492
Examples of GCF
What is the relation between LCM and GCF (Greatest Common Factor)?GCF and LCM of two numbers can be related as GCF(375, 492) = ( 375 * 492 ) / LCM(375, 492) = 3.
What is the GCF of 375 and 492?GCF of 375 and 492 is 3.
Ram has 375 cans of Pepsi and 492 cans of Coca Cola. He wants to create identical refreshment tables that will be organized in his house warming party. He also doesn't want to have any can left over. What is the greatest number of tables that Ram can arrange?To find the greatest number of tables that Ram can stock we need to find the GCF of 375 and 492. Hence GCF of 375 and 492 is 3. So the number of tables that can be arranged is 3.
Rubel is creating individual servings of starters for her birthday party. He has 375 pizzas and 492 hamburgers. He wants each serving to be identical, with no left overs. Can you help Rubel in arranging the same in greatest possible way?The greatest number of servings Rubel can create would be equal to the GCF of 375 and 492. Thus GCF of 375 and 492 is 3.
Ariel is making ready to eat meals to share with friends. She has 375 bottles of water and 492 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 375 and 492. So the GCF of 375 and 492 is 3.
Mary has 375 blue buttons and 492 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 375 and 492. Hence, the GCF of 375 and 492 or the greatest arrangement is 3.
Kamal is making identical balloon arrangements for a party. He has 375 maroon balloons, and 492 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 375 and 492. So the GCF of 375 and 492 is 3.
Kunal is making baskets full of nuts and dried fruits. He has 375 bags of nuts and 492 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 375 and 492. So the GCF of 375 and 492 is 3.
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 375 bus tickets and 492 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 375 and 492. Hence, GCF of 375 and 492 is 3.