Highest Common Factor of 752, 192, 140 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 752, 192, 140 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 752, 192, 140 is 4 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 752, 192, 140 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 752, 192, 140 is 4.
HCF(752, 192, 140) = 4
HCF of 752, 192, 140 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 752, 192, 140 is 4.
Highest Common Factor of 752,192,140 is 4
Step 1: Since 752 > 192, we apply the division lemma to 752 and 192, to get
752 = 192 x 3 + 176
Step 2: Since the reminder 192 ≠ 0, we apply division lemma to 176 and 192, to get
192 = 176 x 1 + 16
Step 3: We consider the new divisor 176 and the new remainder 16, and apply the division lemma to get
176 = 16 x 11 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 16, the HCF of 752 and 192 is 16
Notice that 16 = HCF(176,16) = HCF(192,176) = HCF(752,192) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 140 > 16, we apply the division lemma to 140 and 16, to get
140 = 16 x 8 + 12
Step 2: Since the reminder 16 ≠ 0, we apply division lemma to 12 and 16, to get
16 = 12 x 1 + 4
Step 3: We consider the new divisor 12 and the new remainder 4, and apply the division lemma to get
12 = 4 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 16 and 140 is 4
Notice that 4 = HCF(12,4) = HCF(16,12) = HCF(140,16) .
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Frequently Asked Questions on HCF of 752, 192, 140 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 752, 192, 140?
Answer: HCF of 752, 192, 140 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 752, 192, 140 using Euclid's Algorithm?
Answer: For arbitrary numbers 752, 192, 140 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.