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 650, 923, 54 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 650, 923, 54 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 650, 923, 54 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 650, 923, 54 is 1.
HCF(650, 923, 54) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 650, 923, 54 is 1.
Step 1: Since 923 > 650, we apply the division lemma to 923 and 650, to get
923 = 650 x 1 + 273
Step 2: Since the reminder 650 ≠ 0, we apply division lemma to 273 and 650, to get
650 = 273 x 2 + 104
Step 3: We consider the new divisor 273 and the new remainder 104, and apply the division lemma to get
273 = 104 x 2 + 65
We consider the new divisor 104 and the new remainder 65,and apply the division lemma to get
104 = 65 x 1 + 39
We consider the new divisor 65 and the new remainder 39,and apply the division lemma to get
65 = 39 x 1 + 26
We consider the new divisor 39 and the new remainder 26,and apply the division lemma to get
39 = 26 x 1 + 13
We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get
26 = 13 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 650 and 923 is 13
Notice that 13 = HCF(26,13) = HCF(39,26) = HCF(65,39) = HCF(104,65) = HCF(273,104) = HCF(650,273) = HCF(923,650) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 54 > 13, we apply the division lemma to 54 and 13, to get
54 = 13 x 4 + 2
Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 2 and 13, to get
13 = 2 x 6 + 1
Step 3: 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 13 and 54 is 1
Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(54,13) .
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 650, 923, 54?
Answer: HCF of 650, 923, 54 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 650, 923, 54 using Euclid's Algorithm?
Answer: For arbitrary numbers 650, 923, 54 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.