Highest Common Factor of 750, 900, 212 using Euclid's algorithm
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 750, 900, 212 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 750, 900, 212 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 750, 900, 212 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 750, 900, 212 is 2.
HCF(750, 900, 212) = 2
HCF of 750, 900, 212 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 750, 900, 212 is 2.
Highest Common Factor of 750,900,212 is 2
Step 1: Since 900 > 750, we apply the division lemma to 900 and 750, to get
900 = 750 x 1 + 150
Step 2: Since the reminder 750 ≠ 0, we apply division lemma to 150 and 750, to get
750 = 150 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 150, the HCF of 750 and 900 is 150
Notice that 150 = HCF(750,150) = HCF(900,750) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 212 > 150, we apply the division lemma to 212 and 150, to get
212 = 150 x 1 + 62
Step 2: Since the reminder 150 ≠ 0, we apply division lemma to 62 and 150, to get
150 = 62 x 2 + 26
Step 3: We consider the new divisor 62 and the new remainder 26, and apply the division lemma to get
62 = 26 x 2 + 10
We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get
26 = 10 x 2 + 6
We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get
10 = 6 x 1 + 4
We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get
6 = 4 x 1 + 2
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 150 and 212 is 2
Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(62,26) = HCF(150,62) = HCF(212,150) .
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Frequently Asked Questions on HCF of 750, 900, 212 using Euclid's Algorithm
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 750, 900, 212?
Answer: HCF of 750, 900, 212 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 750, 900, 212 using Euclid's Algorithm?
Answer: For arbitrary numbers 750, 900, 212 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.