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 902, 355, 432 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 902, 355, 432 is 1 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 902, 355, 432 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 902, 355, 432 is 1.
HCF(902, 355, 432) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 902, 355, 432 is 1.
Step 1: Since 902 > 355, we apply the division lemma to 902 and 355, to get
902 = 355 x 2 + 192
Step 2: Since the reminder 355 ≠ 0, we apply division lemma to 192 and 355, to get
355 = 192 x 1 + 163
Step 3: We consider the new divisor 192 and the new remainder 163, and apply the division lemma to get
192 = 163 x 1 + 29
We consider the new divisor 163 and the new remainder 29,and apply the division lemma to get
163 = 29 x 5 + 18
We consider the new divisor 29 and the new remainder 18,and apply the division lemma to get
29 = 18 x 1 + 11
We consider the new divisor 18 and the new remainder 11,and apply the division lemma to get
18 = 11 x 1 + 7
We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get
11 = 7 x 1 + 4
We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get
7 = 4 x 1 + 3
We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get
4 = 3 x 1 + 1
We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 902 and 355 is 1
Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(18,11) = HCF(29,18) = HCF(163,29) = HCF(192,163) = HCF(355,192) = HCF(902,355) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 432 > 1, we apply the division lemma to 432 and 1, to get
432 = 1 x 432 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 432 is 1
Notice that 1 = HCF(432,1) .
Here are some samples of HCF using Euclid's Algorithm calculations.
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 902, 355, 432?
Answer: HCF of 902, 355, 432 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 902, 355, 432 using Euclid's Algorithm?
Answer: For arbitrary numbers 902, 355, 432 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.