Highest Common Factor of 604, 972 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 604, 972 i.e. 4 the largest integer that leaves a remainder zero for all numbers.
HCF of 604, 972 is 4 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, 972 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, 972 is 4.
HCF(604, 972) = 4
HCF of 604, 972 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 604, 972 is 4.
Highest Common Factor of 604,972 is 4
Step 1: Since 972 > 604, we apply the division lemma to 972 and 604, to get
972 = 604 x 1 + 368
Step 2: Since the reminder 604 ≠ 0, we apply division lemma to 368 and 604, to get
604 = 368 x 1 + 236
Step 3: We consider the new divisor 368 and the new remainder 236, and apply the division lemma to get
368 = 236 x 1 + 132
We consider the new divisor 236 and the new remainder 132,and apply the division lemma to get
236 = 132 x 1 + 104
We consider the new divisor 132 and the new remainder 104,and apply the division lemma to get
132 = 104 x 1 + 28
We consider the new divisor 104 and the new remainder 28,and apply the division lemma to get
104 = 28 x 3 + 20
We consider the new divisor 28 and the new remainder 20,and apply the division lemma to get
28 = 20 x 1 + 8
We consider the new divisor 20 and the new remainder 8,and apply the division lemma to get
20 = 8 x 2 + 4
We consider the new divisor 8 and the new remainder 4,and apply the division lemma to get
8 = 4 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 604 and 972 is 4
Notice that 4 = HCF(8,4) = HCF(20,8) = HCF(28,20) = HCF(104,28) = HCF(132,104) = HCF(236,132) = HCF(368,236) = HCF(604,368) = HCF(972,604) .
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Frequently Asked Questions on HCF of 604, 972 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 604, 972?
Answer: HCF of 604, 972 is 4 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 604, 972 using Euclid's Algorithm?
Answer: For arbitrary numbers 604, 972 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.