what is the gcf of 35 and 1,715
35
35
35 goes into 1,715 49 times.
35
To find the greatest common factor (GCF) of 35 and 1,715, we can use the method of prime factorization. Here's how you can find the GCF step by step:
Step 1: Prime factorize both numbers.
- Prime factorization of 35: 5 x 7
- Prime factorization of 1,715: 5 x 7 x 7 x 7
Step 2: Identify the common prime factors.
Both numbers have the prime factors 5 and 7 in common.
Step 3: Find the product of the common prime factors.
The product of the common prime factors 5 and 7 is 5 x 7 = 35.
Therefore, the GCF of 35 and 1,715 is 35.
If you prefer a quicker method, you can also use the Euclidean algorithm. Here's how:
Step 1: Divide the larger number (1,715) by the smaller number (35).
- 1,715 ÷ 35 = 49 with a remainder of 0
Step 2: The divisor from the previous step (35) is the GCF of the original numbers.
Therefore, the GCF of 35 and 1,715 is again 35.