Highest Common Factor of 432, 972, 14 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 432, 972, 14 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 432, 972, 14 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 432, 972, 14 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 432, 972, 14 is 2.
HCF(432, 972, 14) = 2
HCF of 432, 972, 14 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 432, 972, 14 is 2.
Highest Common Factor of 432,972,14 is 2
Step 1: Since 972 > 432, we apply the division lemma to 972 and 432, to get
972 = 432 x 2 + 108
Step 2: Since the reminder 432 ≠ 0, we apply division lemma to 108 and 432, to get
432 = 108 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 108, the HCF of 432 and 972 is 108
Notice that 108 = HCF(432,108) = HCF(972,432) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 108 > 14, we apply the division lemma to 108 and 14, to get
108 = 14 x 7 + 10
Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 10 and 14, to get
14 = 10 x 1 + 4
Step 3: We consider the new divisor 10 and the new remainder 4, and apply the division lemma to get
10 = 4 x 2 + 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 108 and 14 is 2
Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(108,14) .
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Frequently Asked Questions on HCF of 432, 972, 14 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 432, 972, 14?
Answer: HCF of 432, 972, 14 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 432, 972, 14 using Euclid's Algorithm?
Answer: For arbitrary numbers 432, 972, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.