Highest Common Factor of 750, 5208, 1112 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, 5208, 1112 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 750, 5208, 1112 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, 5208, 1112 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, 5208, 1112 is 2.
HCF(750, 5208, 1112) = 2
HCF of 750, 5208, 1112 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, 5208, 1112 is 2.
Highest Common Factor of 750,5208,1112 is 2
Step 1: Since 5208 > 750, we apply the division lemma to 5208 and 750, to get
5208 = 750 x 6 + 708
Step 2: Since the reminder 750 ≠ 0, we apply division lemma to 708 and 750, to get
750 = 708 x 1 + 42
Step 3: We consider the new divisor 708 and the new remainder 42, and apply the division lemma to get
708 = 42 x 16 + 36
We consider the new divisor 42 and the new remainder 36,and apply the division lemma to get
42 = 36 x 1 + 6
We consider the new divisor 36 and the new remainder 6,and apply the division lemma to get
36 = 6 x 6 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 6, the HCF of 750 and 5208 is 6
Notice that 6 = HCF(36,6) = HCF(42,36) = HCF(708,42) = HCF(750,708) = HCF(5208,750) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 1112 > 6, we apply the division lemma to 1112 and 6, to get
1112 = 6 x 185 + 2
Step 2: Since the reminder 6 ≠ 0, we apply division lemma to 2 and 6, 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 6 and 1112 is 2
Notice that 2 = HCF(6,2) = HCF(1112,6) .
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Frequently Asked Questions on HCF of 750, 5208, 1112 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, 5208, 1112?
Answer: HCF of 750, 5208, 1112 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 750, 5208, 1112 using Euclid's Algorithm?
Answer: For arbitrary numbers 750, 5208, 1112 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.