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 918, 385, 109 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 918, 385, 109 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 918, 385, 109 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 918, 385, 109 is 1.
HCF(918, 385, 109) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 918, 385, 109 is 1.
Step 1: Since 918 > 385, we apply the division lemma to 918 and 385, to get
918 = 385 x 2 + 148
Step 2: Since the reminder 385 ≠ 0, we apply division lemma to 148 and 385, to get
385 = 148 x 2 + 89
Step 3: We consider the new divisor 148 and the new remainder 89, and apply the division lemma to get
148 = 89 x 1 + 59
We consider the new divisor 89 and the new remainder 59,and apply the division lemma to get
89 = 59 x 1 + 30
We consider the new divisor 59 and the new remainder 30,and apply the division lemma to get
59 = 30 x 1 + 29
We consider the new divisor 30 and the new remainder 29,and apply the division lemma to get
30 = 29 x 1 + 1
We consider the new divisor 29 and the new remainder 1,and apply the division lemma to get
29 = 1 x 29 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 918 and 385 is 1
Notice that 1 = HCF(29,1) = HCF(30,29) = HCF(59,30) = HCF(89,59) = HCF(148,89) = HCF(385,148) = HCF(918,385) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 109 > 1, we apply the division lemma to 109 and 1, to get
109 = 1 x 109 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 109 is 1
Notice that 1 = HCF(109,1) .
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 918, 385, 109?
Answer: HCF of 918, 385, 109 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 918, 385, 109 using Euclid's Algorithm?
Answer: For arbitrary numbers 918, 385, 109 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.