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 500, 924, 740 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 500, 924, 740 is 4 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 500, 924, 740 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 500, 924, 740 is 4.
HCF(500, 924, 740) = 4
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 500, 924, 740 is 4.
Step 1: Since 924 > 500, we apply the division lemma to 924 and 500, to get
924 = 500 x 1 + 424
Step 2: Since the reminder 500 ≠ 0, we apply division lemma to 424 and 500, to get
500 = 424 x 1 + 76
Step 3: We consider the new divisor 424 and the new remainder 76, and apply the division lemma to get
424 = 76 x 5 + 44
We consider the new divisor 76 and the new remainder 44,and apply the division lemma to get
76 = 44 x 1 + 32
We consider the new divisor 44 and the new remainder 32,and apply the division lemma to get
44 = 32 x 1 + 12
We consider the new divisor 32 and the new remainder 12,and apply the division lemma to get
32 = 12 x 2 + 8
We consider the new divisor 12 and the new remainder 8,and apply the division lemma to get
12 = 8 x 1 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 500 and 924 is 4
Notice that 4 = HCF(8,4) = HCF(12,8) = HCF(32,12) = HCF(44,32) = HCF(76,44) = HCF(424,76) = HCF(500,424) = HCF(924,500) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 740 > 4, we apply the division lemma to 740 and 4, to get
740 = 4 x 185 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 740 is 4
Notice that 4 = HCF(740,4) .
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 500, 924, 740?
Answer: HCF of 500, 924, 740 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 500, 924, 740 using Euclid's Algorithm?
Answer: For arbitrary numbers 500, 924, 740 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.