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 751, 905, 20 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 751, 905, 20 is 1 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 751, 905, 20 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 751, 905, 20 is 1.
HCF(751, 905, 20) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 751, 905, 20 is 1.
Step 1: Since 905 > 751, we apply the division lemma to 905 and 751, to get
905 = 751 x 1 + 154
Step 2: Since the reminder 751 ≠ 0, we apply division lemma to 154 and 751, to get
751 = 154 x 4 + 135
Step 3: We consider the new divisor 154 and the new remainder 135, and apply the division lemma to get
154 = 135 x 1 + 19
We consider the new divisor 135 and the new remainder 19,and apply the division lemma to get
135 = 19 x 7 + 2
We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get
19 = 2 x 9 + 1
We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get
2 = 1 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 751 and 905 is 1
Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(135,19) = HCF(154,135) = HCF(751,154) = HCF(905,751) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 20 > 1, we apply the division lemma to 20 and 1, to get
20 = 1 x 20 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 20 is 1
Notice that 1 = HCF(20,1) .
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 751, 905, 20?
Answer: HCF of 751, 905, 20 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 751, 905, 20 using Euclid's Algorithm?
Answer: For arbitrary numbers 751, 905, 20 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.