Highest Common Factor of 750, 825, 114 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, 825, 114 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 750, 825, 114 is 3 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, 825, 114 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, 825, 114 is 3.
HCF(750, 825, 114) = 3
HCF of 750, 825, 114 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, 825, 114 is 3.
Highest Common Factor of 750,825,114 is 3
Step 1: Since 825 > 750, we apply the division lemma to 825 and 750, to get
825 = 750 x 1 + 75
Step 2: Since the reminder 750 ≠ 0, we apply division lemma to 75 and 750, to get
750 = 75 x 10 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 75, the HCF of 750 and 825 is 75
Notice that 75 = HCF(750,75) = HCF(825,750) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 114 > 75, we apply the division lemma to 114 and 75, to get
114 = 75 x 1 + 39
Step 2: Since the reminder 75 ≠ 0, we apply division lemma to 39 and 75, to get
75 = 39 x 1 + 36
Step 3: We consider the new divisor 39 and the new remainder 36, and apply the division lemma to get
39 = 36 x 1 + 3
We consider the new divisor 36 and the new remainder 3, and apply the division lemma to get
36 = 3 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 75 and 114 is 3
Notice that 3 = HCF(36,3) = HCF(39,36) = HCF(75,39) = HCF(114,75) .
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Frequently Asked Questions on HCF of 750, 825, 114 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, 825, 114?
Answer: HCF of 750, 825, 114 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 750, 825, 114 using Euclid's Algorithm?
Answer: For arbitrary numbers 750, 825, 114 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.