Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 945, 135, 785 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 945, 135, 785 is 5 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 945, 135, 785 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 945, 135, 785 is 5.
HCF(945, 135, 785) = 5
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 945, 135, 785 is 5.
Step 1: Since 945 > 135, we apply the division lemma to 945 and 135, to get
945 = 135 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 135, the HCF of 945 and 135 is 135
Notice that 135 = HCF(945,135) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 785 > 135, we apply the division lemma to 785 and 135, to get
785 = 135 x 5 + 110
Step 2: Since the reminder 135 ≠ 0, we apply division lemma to 110 and 135, to get
135 = 110 x 1 + 25
Step 3: We consider the new divisor 110 and the new remainder 25, and apply the division lemma to get
110 = 25 x 4 + 10
We consider the new divisor 25 and the new remainder 10,and apply the division lemma to get
25 = 10 x 2 + 5
We consider the new divisor 10 and the new remainder 5,and apply the division lemma to get
10 = 5 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 135 and 785 is 5
Notice that 5 = HCF(10,5) = HCF(25,10) = HCF(110,25) = HCF(135,110) = HCF(785,135) .
Here are some samples of HCF using Euclid's Algorithm calculations.
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 945, 135, 785?
Answer: HCF of 945, 135, 785 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 945, 135, 785 using Euclid's Algorithm?
Answer: For arbitrary numbers 945, 135, 785 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.