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 742, 421, 932 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 742, 421, 932 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 742, 421, 932 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 742, 421, 932 is 1.
HCF(742, 421, 932) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 742, 421, 932 is 1.
Step 1: Since 742 > 421, we apply the division lemma to 742 and 421, to get
742 = 421 x 1 + 321
Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 321 and 421, to get
421 = 321 x 1 + 100
Step 3: We consider the new divisor 321 and the new remainder 100, and apply the division lemma to get
321 = 100 x 3 + 21
We consider the new divisor 100 and the new remainder 21,and apply the division lemma to get
100 = 21 x 4 + 16
We consider the new divisor 21 and the new remainder 16,and apply the division lemma to get
21 = 16 x 1 + 5
We consider the new divisor 16 and the new remainder 5,and apply the division lemma to get
16 = 5 x 3 + 1
We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get
5 = 1 x 5 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 742 and 421 is 1
Notice that 1 = HCF(5,1) = HCF(16,5) = HCF(21,16) = HCF(100,21) = HCF(321,100) = HCF(421,321) = HCF(742,421) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 932 > 1, we apply the division lemma to 932 and 1, to get
932 = 1 x 932 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 932 is 1
Notice that 1 = HCF(932,1) .
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 742, 421, 932?
Answer: HCF of 742, 421, 932 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 742, 421, 932 using Euclid's Algorithm?
Answer: For arbitrary numbers 742, 421, 932 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.