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 921, 732, 63 i.e. 3 the largest integer that leaves a remainder zero for all numbers.
HCF of 921, 732, 63 is 3 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 921, 732, 63 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 921, 732, 63 is 3.
HCF(921, 732, 63) = 3
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 921, 732, 63 is 3.
Step 1: Since 921 > 732, we apply the division lemma to 921 and 732, to get
921 = 732 x 1 + 189
Step 2: Since the reminder 732 ≠ 0, we apply division lemma to 189 and 732, to get
732 = 189 x 3 + 165
Step 3: We consider the new divisor 189 and the new remainder 165, and apply the division lemma to get
189 = 165 x 1 + 24
We consider the new divisor 165 and the new remainder 24,and apply the division lemma to get
165 = 24 x 6 + 21
We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get
24 = 21 x 1 + 3
We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get
21 = 3 x 7 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 921 and 732 is 3
Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(165,24) = HCF(189,165) = HCF(732,189) = HCF(921,732) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 63 > 3, we apply the division lemma to 63 and 3, to get
63 = 3 x 21 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 3 and 63 is 3
Notice that 3 = HCF(63,3) .
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 921, 732, 63?
Answer: HCF of 921, 732, 63 is 3 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 921, 732, 63 using Euclid's Algorithm?
Answer: For arbitrary numbers 921, 732, 63 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.