Highest Common Factor of 304, 172, 972 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 304, 172, 972 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 304, 172, 972 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 304, 172, 972 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 304, 172, 972 is 4.
HCF(304, 172, 972) = 4
HCF of 304, 172, 972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 304, 172, 972 is 4.
Highest Common Factor of 304,172,972 is 4
Step 1: Since 304 > 172, we apply the division lemma to 304 and 172, to get
304 = 172 x 1 + 132
Step 2: Since the reminder 172 ≠ 0, we apply division lemma to 132 and 172, to get
172 = 132 x 1 + 40
Step 3: We consider the new divisor 132 and the new remainder 40, and apply the division lemma to get
132 = 40 x 3 + 12
We consider the new divisor 40 and the new remainder 12,and apply the division lemma to get
40 = 12 x 3 + 4
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 304 and 172 is 4
Notice that 4 = HCF(12,4) = HCF(40,12) = HCF(132,40) = HCF(172,132) = HCF(304,172) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 972 > 4, we apply the division lemma to 972 and 4, to get
972 = 4 x 243 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 972 is 4
Notice that 4 = HCF(972,4) .
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Frequently Asked Questions on HCF of 304, 172, 972 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 304, 172, 972?
Answer: HCF of 304, 172, 972 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 304, 172, 972 using Euclid's Algorithm?
Answer: For arbitrary numbers 304, 172, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
