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 (175, 315).
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 175 and 315, such that GCF is 35 where 35 will always be less than 175 and 315.
- 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 175 x 0 = 0 and 315 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, 25, 35, 175 are exact divisors of 175 and 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315 are exact divisors of 315.
- Factors of 175 are 1, 5, 7, 25, 35, 175. Each factor divides 175 without leaving a remainder.
Simlarly, factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315. Each factor divides 315 without leaving a remainder.
Steps to find Factors of 175 and 315
- Step 1. Find all the numbers that would divide 175 and 315 without leaving any remainder. Starting with the number 1 upto 87 (half of 175) and 1 upto 157 (half of 315). The number 1 and the number itself are always factors of the given number.
175 ÷ 1 : Remainder = 0
315 ÷ 1 : Remainder = 0
175 ÷ 5 : Remainder = 0
315 ÷ 3 : Remainder = 0
175 ÷ 7 : Remainder = 0
315 ÷ 5 : Remainder = 0
175 ÷ 25 : Remainder = 0
315 ÷ 7 : Remainder = 0
175 ÷ 35 : Remainder = 0
315 ÷ 9 : Remainder = 0
175 ÷ 175 : Remainder = 0
315 ÷ 15 : Remainder = 0
315 ÷ 105 : Remainder = 0
315 ÷ 315 : Remainder = 0
Hence, Factors of
175 are 1, 5, 7, 25, 35, and 175
And, Factors of
315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, and 315
Examples of GCF
Sammy baked 175 chocolate cookies and 315 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 175 and 315.
GCF of 175 and 315 is 35.
A class has 175 boys and 315 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 175 and 315. Hence, GCF of 175 and 315 is 35.
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(175, 315) = ( 175 * 315 ) / LCM(175, 315) = 35.
What is the GCF of 175 and 315?GCF of 175 and 315 is 35.
Mary has 175 blue buttons and 315 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 175 and 315. Hence, the GCF of 175 and 315 or the greatest arrangement is 35.
Kamal is making identical balloon arrangements for a party. He has 175 maroon balloons, and 315 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 175 and 315. So the GCF of 175 and 315 is 35.
Kunal is making baskets full of nuts and dried fruits. He has 175 bags of nuts and 315 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 175 and 315. So the GCF of 175 and 315 is 35.
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 175 bus tickets and 315 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 175 and 315. Hence, GCF of 175 and 315 is 35.