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 604, 352, 921 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 604, 352, 921 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 604, 352, 921 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 604, 352, 921 is 1.
HCF(604, 352, 921) = 1
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 604, 352, 921 is 1.
Step 1: Since 604 > 352, we apply the division lemma to 604 and 352, to get
604 = 352 x 1 + 252
Step 2: Since the reminder 352 ≠ 0, we apply division lemma to 252 and 352, to get
352 = 252 x 1 + 100
Step 3: We consider the new divisor 252 and the new remainder 100, and apply the division lemma to get
252 = 100 x 2 + 52
We consider the new divisor 100 and the new remainder 52,and apply the division lemma to get
100 = 52 x 1 + 48
We consider the new divisor 52 and the new remainder 48,and apply the division lemma to get
52 = 48 x 1 + 4
We consider the new divisor 48 and the new remainder 4,and apply the division lemma to get
48 = 4 x 12 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 604 and 352 is 4
Notice that 4 = HCF(48,4) = HCF(52,48) = HCF(100,52) = HCF(252,100) = HCF(352,252) = HCF(604,352) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 921 > 4, we apply the division lemma to 921 and 4, to get
921 = 4 x 230 + 1
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 1 and 4, to get
4 = 1 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 4 and 921 is 1
Notice that 1 = HCF(4,1) = HCF(921,4) .
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 604, 352, 921?
Answer: HCF of 604, 352, 921 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 604, 352, 921 using Euclid's Algorithm?
Answer: For arbitrary numbers 604, 352, 921 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.