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 912, 240, 734 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 912, 240, 734 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 912, 240, 734 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 912, 240, 734 is 2.
HCF(912, 240, 734) = 2
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 912, 240, 734 is 2.
Step 1: Since 912 > 240, we apply the division lemma to 912 and 240, to get
912 = 240 x 3 + 192
Step 2: Since the reminder 240 ≠ 0, we apply division lemma to 192 and 240, to get
240 = 192 x 1 + 48
Step 3: We consider the new divisor 192 and the new remainder 48, and apply the division lemma to get
192 = 48 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 48, the HCF of 912 and 240 is 48
Notice that 48 = HCF(192,48) = HCF(240,192) = HCF(912,240) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 734 > 48, we apply the division lemma to 734 and 48, to get
734 = 48 x 15 + 14
Step 2: Since the reminder 48 ≠ 0, we apply division lemma to 14 and 48, to get
48 = 14 x 3 + 6
Step 3: We consider the new divisor 14 and the new remainder 6, and apply the division lemma to get
14 = 6 x 2 + 2
We consider the new divisor 6 and the new remainder 2, and apply the division lemma to get
6 = 2 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 48 and 734 is 2
Notice that 2 = HCF(6,2) = HCF(14,6) = HCF(48,14) = HCF(734,48) .
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 912, 240, 734?
Answer: HCF of 912, 240, 734 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 912, 240, 734 using Euclid's Algorithm?
Answer: For arbitrary numbers 912, 240, 734 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.