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 744, 256, 680 i.e. 8 the largest integer that leaves a remainder zero for all numbers.
HCF of 744, 256, 680 is 8 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 744, 256, 680 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 744, 256, 680 is 8.
HCF(744, 256, 680) = 8
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 744, 256, 680 is 8.
Step 1: Since 744 > 256, we apply the division lemma to 744 and 256, to get
744 = 256 x 2 + 232
Step 2: Since the reminder 256 ≠ 0, we apply division lemma to 232 and 256, to get
256 = 232 x 1 + 24
Step 3: We consider the new divisor 232 and the new remainder 24, and apply the division lemma to get
232 = 24 x 9 + 16
We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get
24 = 16 x 1 + 8
We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get
16 = 8 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 744 and 256 is 8
Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(232,24) = HCF(256,232) = HCF(744,256) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 680 > 8, we apply the division lemma to 680 and 8, to get
680 = 8 x 85 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 8 and 680 is 8
Notice that 8 = HCF(680,8) .
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 744, 256, 680?
Answer: HCF of 744, 256, 680 is 8 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 744, 256, 680 using Euclid's Algorithm?
Answer: For arbitrary numbers 744, 256, 680 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.