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, 516, 160 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 918, 516, 160 is 2 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, 516, 160 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, 516, 160 is 2.
HCF(918, 516, 160) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 918, 516, 160 is 2.
Step 1: Since 918 > 516, we apply the division lemma to 918 and 516, to get
918 = 516 x 1 + 402
Step 2: Since the reminder 516 ≠ 0, we apply division lemma to 402 and 516, to get
516 = 402 x 1 + 114
Step 3: We consider the new divisor 402 and the new remainder 114, and apply the division lemma to get
402 = 114 x 3 + 60
We consider the new divisor 114 and the new remainder 60,and apply the division lemma to get
114 = 60 x 1 + 54
We consider the new divisor 60 and the new remainder 54,and apply the division lemma to get
60 = 54 x 1 + 6
We consider the new divisor 54 and the new remainder 6,and apply the division lemma to get
54 = 6 x 9 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 918 and 516 is 6
Notice that 6 = HCF(54,6) = HCF(60,54) = HCF(114,60) = HCF(402,114) = HCF(516,402) = HCF(918,516) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 160 > 6, we apply the division lemma to 160 and 6, to get
160 = 6 x 26 + 4
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 4 and 6, to get
6 = 4 x 1 + 2
Step 3: We consider the new divisor 4 and the new remainder 2, and apply the division lemma to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6 and 160 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(160,6) .
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, 516, 160?
Answer: HCF of 918, 516, 160 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 918, 516, 160 using Euclid's Algorithm?
Answer: For arbitrary numbers 918, 516, 160 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.