Mathematics · Greatest common factor
GCF of 35 and 56
The greatest common factor of 35 and 56 is 7. It is the largest whole number that divides both 35 and 56 with no remainder.
You will also see it written as the highest common factor (HCF) or the greatest common divisor (GCD) of 35 and 56. All three names mean the same thing.
Greatest common factor
7
GCF, GCD or HCF of 35 and 56
Least common multiple
280
LCM of 35 and 56
35/56 simplified
5/8
both divided by 7
Below is the same answer reached three different ways, because different classes teach different methods. Every line is worked out for these two numbers, so you can copy the one your teacher asks for.
Listing the factors of 35 and 56
Factors of 35: 1, 5, 7, 35
Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
Common factors: 1, 7
Greatest of those = 7
The common factors of 35 and 56 are 1 and 7, and that is the complete list. The largest one, 7, is the GCF.
Prime factorization method
35 = 5 × 7 (5 × 7)
56 = 23 × 7 (2 × 2 × 2 × 7)
Shared primes at their lowest power: 7
GCF = 7
Only 7 appears in both lists, and only once in each, so nothing else carries over and the GCF is 7.
Euclid's algorithm, step by step
56 ÷ 35 = 1 remainder 21
35 ÷ 21 = 1 remainder 14
21 ÷ 14 = 1 remainder 7
14 ÷ 7 = 2 remainder 0
Last non-zero remainder = 7, so the GCF is 7
Divide the larger number by the smaller, then keep dividing the previous divisor by the remainder. When the remainder reaches zero, the divisor you used last is the GCF. It took 4 steps for 35 and 56.
LCM of 35 and 56, and the fraction 35/56
For any two numbers, the GCF multiplied by the LCM equals the two numbers multiplied together. That gives a quick way to get one from the other, and a way to check both.
GCF × LCM = 7 × 280 = 1,960
35 × 56 = 1,960
They match, so both answers are right
Dividing the top and bottom of 35/56 by 7 reduces it to 5/8, which is as far as it goes. Anything smaller than the GCF would leave the fraction reducible.
GCF of 35 and 56: FAQs
What is the GCF of 35 and 56?
The GCF of 35 and 56 is 7. It is the largest whole number that divides both of them exactly.
What are the common factors of 35 and 56?
The common factors of 35 and 56 are 1 and 7. The greatest of them is 7.
Is the GCF of 56 and 35 the same as the GCF of 35 and 56?
Yes. The order makes no difference. The greatest common factor of 56 and 35 is 7, exactly the same as the GCF of 35 and 56, because you are looking at the same two numbers either way. The same is true if you see it written as the highest common factor of 56 and 35.
What is the LCM of 35 and 56?
The LCM of 35 and 56 is 280. You can check it with GCF times LCM: 7 times 280 equals 1,960, which is the same as 35 times 56.
Are 35 and 56 coprime?
No. 35 and 56 share 7 as a common factor, so they are not coprime. Coprime numbers have a GCF of exactly 1.
How do you simplify 35/56?
Divide the top and the bottom by their GCF, which is 7. That gives 35 divided by 7 equals 5, and 56 divided by 7 equals 8, so 35/56 simplifies to 5/8.
Which method is quickest for 35 and 56?
Euclid's algorithm, because it reaches the answer in 4 steps and you never have to write out the full factor lists.
Nearby pairs
Any other numbers? The GCF Calculator takes two to ten values and shows the same three methods, and the math calculators page has the rest of the set.
Open the GCF Calculator →
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